How do I determine if this equation is a linear function or a nonlinear function?
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A linear equation has the following form:
y = mx + b
where
m is the slope
b is the y-intercept.
You can also perform a vertical line test. If the line touches your graphed function in more than one spot, it is not a function.
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The variable x must be either degree zero or degree 1 AND the variable y must be 1st degree in order to be a linear function.
Examples:
y = 2x - 3 (both x and y are 1st degree)
4x + 5y = 20 (both x and y are first degree)
2x - 4y = 7 + 3x (all variables are 1st degree)
y = -1 (x is degree zero and y is 1st degree; this makes a horizontal line which is a function of x)
If variable x is 1st degree but the variable y has a degree of zero, it will be a linear relation but not a function of x.
Example:
x = 4 (the graph is a vertical line and is not a function of x)
If variable y is 1st degree but the variable x has a degree other than 0 or 1, it will be a non-linear function of x.
Examples:
y = x^2 + 25 (x is not first degree)
y = 5x + 2 - x^3 (x is 3rd degree)
y = 1/x or y = x^(-1) (x is to the power of -1)
y = sqrt(x) or y = x^(1/2) (x is to the 1/2 power; the graph is 1/2 a sideways parabola)
y = 2^x (x is the exponent instead of the base, so the graph is exponential and not linear)
If variable y is not 1st degree, the relation will not be a function of x.
Example:
x^2 + y^2 = 4 (neither x nor y is 1st degree; the graph is a circle with a radius of 2)
x = y^2 (y is not 1st degree; this is a sideways parabola)
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The way how you differentiate a linear and a non linear function is as under-
In a linear equation the variables appear in first degree only and terms containing product of variables are absent.
e.g. y= 2x+3,
y= -3x+4,
3 y=2x-4 etc.
But in case of non linear equations at least one variable is not of the first degree or the equation contain product of variables.
e.g. y=x^2+2,
or, y^2=2x-4,
or, y=2x+3xy-4,
or, xy=1 etc.
``
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An equation is linear if its graph forms a straight line. This will happen when the highest power of x is "1".
Here are a few examples of linear equations:
3x + 2y = 8
y = 2x + 3
y - 2 = 3(x - 1)
(note: all variables are raised to the first degree)
Here are some examples of non-linear equations:
y = x^2 (note: x is raised to the second power)
x^2 + y^2 = 4 (note: both x & y are raised to the second power)
An equation is linear if its graph forms a straight line. This will happen when the highest power of x is "1".
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Graphically, if the equation gives you a straight line thenit is a linear equation. Else if it gives you a circle, or parabola or any other conic for that matter it is a quadratic or nonlinear equation.
ALTERNATIVE:
If the highest power of x in the equation(in...
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To determine you have a linear equation first try your best to get the equation in the following form:
it is typically in the form of y=mx + b
m=slope (rise/run), needs to be constant
b=where the line intersects the y-axis
Then look at your exponent.
The exponent of the variable (x) in an equation tells you the type of equation it is. a variable to the 1st power means the equation is linear, a variable to the 2nd power is a parabola, etc.
There are actually multiple ways to check if an equation or graph is a linear function or not . First make sure that graph fits the equation y = mx + b . y = the point for y ; x = the point for x ; m = slope ; b = y intercept . By using this equation you'll be able to tell if it is a linear line or not . You can also look at the graph to see if it has any curves at all . A linear line must not have any curves at all in the graph .
The way to tell if an equation is linear is by using y = mx + b. M and b can stand for any number as long it stays the same number for one equation. If the equation has a structure like this, then the equation is always linear. If an equation also has a structure like this : mx = y, then the equation is linear. These equations are linear because they grow at a constant rate. One way to tell if an equation is nonlinear, is if it has an exponent in it. Since exponents grow at different rates, the equation would not be linear.
if the x in the equation is not squared or multiplied by its self. so linear looks like x+any number= where non linear is x^any number
If an equation is linear when graphed it will display a line going either upward or downward. the equation itself wouldn't have exponents and the only exponent it would have is to the power of 1.
a nonlinear function would show a graph that isn't a line or a parabola. The equation would include exponents.
The easiest way I have for knowing the difference between linear and nonlinear is the exponent value on the variable x.
If the equation has an x value to the exponent one, it is a linear equation. For example:
y = 2x + 5
If the equation has an x value to the exponent two, it is a parabola. For example:
y = 3x^2 +5x + 3
If x is by itself or equals to 1 then it is a linear function and for it to be non linear then the line on the graph is curved
If the x is by itself then it is a linear function like in the case of y=mx+b case where x has no exponents if x does have exponents besides one then it is not linear.
If the graph plotted isn't in the form of a curve, then it is a linear graph, and thus a linear function.
A linear function is just a straight line. The general formula for a linear function is represented by the equation y=mx+b. This type of equation is set in slope-intercept form, which is the most common form you will see. M represents the slope, or how steep the line is, and B represents where the line crosses to y-axis, or the y-intercept. An example of a linear equation would be y=2x+1. A nonlinear function would be anything that is not a straight line.
y=mx+c
M: the gradient
C: the y intercept
If you see an equation in this form or are given similarly related values then it is.most probably a linear function.
A function is usually linear if it follows a similar format of
y = mx +b. what you have to notice here is the X, if the X has no exponents on it, then it is usually linear, but if the X is X squared or higher then it would not be a linear function.``
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What makes a function linear or non-linear is by the exponent value on the variable x.
A linear function has x with an exponent value of 1. This is a line
A non-linear function has exponent value of x > 1.
For example, consider `y=x`
x has an exponent value of 1. The graph is a straight line through the origin. This graph is linear.
Now consider `y=x^2`
x has an exponent value of 2. The graph is a parabola and not a straight line, and is therefore non-linear.
A linear equation has the following form:
y = mx + c
where
m is the gradient
c is the y-intercept.
y=mx+b form is linear and anything other than that is nonlinear
This only works if you have graphed the equation, then use a Pencil Test to figure out if its a function or not.
Simply-
Line the pencil vertcially with the graph (parellel to Y-axis).
Run the pencil across the graph.
IF, at any point, the your graph touchs the pencil twice, then its NOT a function. If it doesnt, then it is a function.
If the function is in the form of y=mx+b (m(slope)& b=constant ie. 1,2,etc) then its linear
whereas if its in y=ax^2 + bx +c : Quadratic
ax^3+bx^2+cx+d= Cubic
so all functions if they are not in the form of y=mx+b or y=5x+2 then they are not linear
for ex- y=4/x is not linear wherea y=4x is linear for c=0
If it is a linear equation, the highest power the you can see is 1 For example: y=2x-3, 3y=10x+8
non-linear equation can be quadratic, cubic, quartic equations
Linear function is a 1st degree function, meaning the exponent of x is 1. Any exponent for x such as negative, positive that is greater than 1 is not linear.
examples:
y=2x + 1, since the exponent of x is 1 it is a linear function
y= 2x^3, since the exponent of x is 3 it is not linear function
y = 4, it is considered linear, since we can rewrite this as y =0x + 4
y=1/x + 2, it is not linear since x is at the denominator, we expresed in standard form it will become y =x^-1 + 2
y= 2x^(2/3) is not a linear since it has a fractional exponent that is not equivalent to 1.
a linear equation is an application f : R -----> R ( R reals field)
verifies:
x, y `in` R `rArr` f(x) - f(y) = k ( x - y) where k is a costant.
All linear functions are in the form
ax+by = c where a,b,c are real values and x,y are variables.
Does this help?
It's simple: The basic form of a linear function is f(x) = ax + b.
a = the constant
x = the variable
b = the y value
If a is not raised to any power greater than one, than the function is linear. However, for example, if the equation is:
f(x) = ax^2 + b
than the equation is no longer linear, but instead quadratic. It moves up from there, but as long as there are no exponants, your function is linear!
when trying to determine if a given function is linear our not, look at the exponetial of the unknown. If it is NOT 1 then is is NOT linear. If it is exactly 1 then it is linear.
E.g. f(x) = a*x+b is linear. (no listed exponent, so we take it to be 1)
F(x) = a*x^2-b*x+c would be non-linear.
I really do not get how to explain it, so here is an example and a worksheet that you can print out and pr ctice with!! You are welcome!! :)
If the rate of change is constant, then its linear but if its not constant, then its nonlinear.
it is not necessary that it has to be eqn in one variable.
a general 2nd degree eqn like ax^2 + by^2 + 2hxy +2gx +2fy+c=0
represents any curve( line, circle, para hyper bola etc). even if
ax^2 + by^2 =0 then also the eqn is second degree as max power is 2 in 2hxy where poer of x and y is one and1+1=2.
if even 2hxy=0 u can easily see that it becaomes a st line eqn.
if the variavle of the function has power 1 than the function is linear,
that is suppose the function is f(x) = a x^n + b x^m + ...
you check, if at least one of the power of "x" in the whole expression if not "1" then its non-linear, but if all the powers of "x" are either "0" or "1" then its linear.
examples:
1) f(x) = a x + b = a x^1 + b x^0, power of x are 1 & 0 so linear.
2) f(x) = a x + b x^(0.5), powers of x are 1 & 0.5 so non linear.
3) f(x) = a x^100 + b, powers of at least one of the x is 100 =/= 1 so non linear.
4) f(x) = a, power of x is "0" so linear.
Well, if the expression of the function is like this:
f(x)=ax+b
then it is for sure a linear function.
So, all expressions, where it could be found the unknown x, but with the condition that the exponent of the unknown x, not to be bigger than 1, are expressions of linear functions.
the exponent value of x.
A linear function will be a straight line with an x and y intercept and the same slope through the whole line.
A nonlinear function will not be a straight line and will have an indefinite slope.
If y=x+c it is linear regardless of the gradient.
If y＝x^z+c it is not a line. Hence the term non-linear. y=x^2 is a parabola.
There are two ways by which we can test if a given equation is a linear function or not .
1) By Graph : I the graph of the equation is a straight line then the function is a linear function.
ii) By form of the equation : If the degree of the equqtion is one i.e. The power or the exponent of the variable is 1 then the equation is linear. In this case the equation will be in the form : y = mx + c [ where m is the slope of the line and c is the y- intercept ] .
Linear functions come in the form y=ax+b
They are straight lines.
Quadratic functions come in the form y=ax^2 + bx + c
They are parabolas.
Linear equation means equation that plots straight lines on graph.It is of the form ax+by+c=0 where a,b,c are real numbers and x and y variables.
If it can fit the form Ax+By=C it is a linear function, this means no exponents in this form.
check out if the power of x is one
if the x is to the power of one, it is linear(can be written in the form y=mx+b).
unless it Is a absolute value equation (y=|x| or some variation there of)
PS the vertical line test shows when something is a function, not whether it is linear or non-linear
if it uses: y=mc+c, it is linear. A non-linear function will include powers/indices
Find all the variables. If no variable has a power of >1, the function is lenear.
VLT, the vertical line test. Draw a line verticly through all the points graphed. If two points are on the same line, the entire equation isn't a linear function
if you are presented with a table of values, you can determine that the function is linear if it has a constant rate of change, to test this you would take
f(xx)-f(x)/xx-x (This is supposed to be "(f of x-two minus f of x-one), divided by (x-two minus x-one)
-if you do this with multiple ordered pairs given in the table and you get the same answer each time, then you have yourself a linear function.
for example: you are given (1, 5) (2, 10) and (3, 15)
(10-5)/(2-1)= 5 and
(15-10)/(3-2)= 5
you have a constant rate of change is 5 and therefore this formula [f(x)= 5x] is a linear function
A linear function is in the form y = mx + b or f(x) = mx + b, where m is the slope or rate of change and b is the y-intercept or where the graph of the line crosses the y axis. You will notice that this function is degree 1 meaning that the x variable has an exponent of 1. If a function is nonlinear, then the exponent of the x variable would have an exponent of something other than 0 or 1. Another linear function is in the form of y = a or f(x) = a, where is any real number. The exponent of x in this function is 0 because x^0 = 1, ie y = ax^0 or y = 1x.
A good way to tell if it is a linear function or not is to graph it. After graphing it, use the verticle line test to decide wether not it is a function. draw a line from top of the graph to the bottom, if the line crosses your verticle line more than once it is not a function.
another way to decide if it is or not is to make a table. if two x values are the same it is not a function.
Its a single line
y=m(x)+b
* more than or equal to 2 (not>2)
The x has to have a power of 1
if you have a table of values find your first differences. if your first diffs are the same it is linear. if not it is not linear.
If an equation is a linear function then when graphed, it creates a line. Solve the equation so that it takes the form y=mx + b. m is going to be the slope of the equation and show how steep the line is. b will tell you where the y intercept is.
If the equation will not simplify into the y=mx+b form, it is not a linear equation, or you have made a mathematical error. Linear equations will never be raised to a power ie: x2 once simplified. Don't let an equation that IS raised to a power trick you though! Be sure to see if any terms cancel themselves out before you judge it to be linear.
To graph an equation, make a chart with your x and y values. Plug in values for x and then solve the equation and obtain the y value. Finally, chart the results on a coordinate grid to show the path of the line. You only need 2 points to make a line, but a third point is advised just to make sure you've really gotten a straight line!
Happy mathing! Good luck!
probably the easiest way for me is to plug in the equation on a graphing calculator and see if its linear
Hi,
How do I determine if this equation is a linear function or a nonlinear function?
Answer:
Points:
1) If the Power Of variable is 1, so the function is linear.
Example:
Y=mx+b and Y=ax+by+C
2)Generally In mathematics a, b,c are treated as a constant and x,y,z are treated as a variable.
4) If the Power Of variable is greater than 1, so the function is not linear.It can be Quardratic Function or other.
Thanks Alot.
From: Osama khan
all linear functions are in the form
ax+by = c where a,b,c are real values and x,y are variables.
Any equation having both the the degrees of both the variables as one can be called as a linear equation.Otherwise its a non linear equation.
However sometimes you encounter problems having dy/dx & dx/dy instead of x & y these equations are called as differential equations.
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a function like
f(x)=ax+b is a linear function
here expression 'x' have power=1
functions like
f(x)=ax^+bx+c
are non linear functions
linear means single
when a function is like
f(x)=ax+b
then it is called a linear function
LINEAR MEANS SINGLE. WHEN A FUNCTION IS LIKE
f(x)=ax+b
then it is linear function becasue here expression 'x' raises to power '1' only such functions are linear functions and others where exponent 'x' have power greater than one these are non linear functions
* more than or equal to 2 (not >2)
linear function: y=mx+c, x has power 1
nonlinear: x has a power >2, for example, (x+a)(x+b) where if you expand it it becomes x^2 + bx + ax + ab
you would graph your function first.
If it is a straight line then you know its a linear function.
But if it does not make a straight line it is a nonlinear function.
The best way is to use a ruler after you graph and see if its straight.
Well, if the expression of the function is like this:
f(x)=ax+b
then it is for sure a linear function.
So, all expressions, where it could be found the unknown x, but with the condition that the exponent of the unknown x, not to be bigger than 1, are expressions of linear functions.
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