What is the equation of a line that passes through the point (3,-4) and has a slope of 2?
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calendarEducator since 2009
write6 answers
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y + 4=2(x-3)
y+4=2x-6
y=2x-10
2x-y-10=0
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calendarEducator since 2009
write278 answers
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The equation for a line is y = m*x + b, where a point is represented by (x,y), m is the slope, and b is the y intercept (i.e. when x = 0, y = b). So plug in...
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y + 4=2(x-3)
y+4=2x-6
y=2x-10
2x-y-10=0
y = 2x - 10
(3,-4) and has a slope of 2
the slope intercept form is y = mx + b
to find the answe just use this formula : y = a( x + h ) + k
(3(h) , -4(k) ) slope of 2(a)
plug it in
y = 2 (x - 3) -4
y = 2x - 6 - 4
y = 2x - 10
So you are given point (3, -4) and slope 2.
y=mx+b is the basic equation for linear graphs, and in this equation, b is the y-intercept, m is the slope, and y and x are where you can substitute your points.
so you then have y=2x+b. you then substitute your points in the approopriate x and y section to give you: -4=2(3)+b
-4=6+b
-10=b this is our y-intercept, the only thing that was missing to complete our equation, so then our equation would be
y=2X-10
x1=3, y1=-4, m=2
therefore, y-y1=m(x-x1)
=> y+4=2(x-3)
=> y+4=2x-6
=> -2x+y=-10
=> 2x-y=10
The other methods given here all yield correct equations, however the name of the form used in some of these solutions is not.
The Slope-Intercept Form of a linear equation is:
y=mx+b,
where m is the slope of the line, and b is the y-intercept of the line. x and y are the coordinates of any point on the line, (x,y).
You could plug the slope (2) in for m, and the x (3) and y (-4) values for the given point in for x and y, then solve for the missing value, b (our y-intercept).
-4 = 2(3)+b
-4 = 6+b then subtract 6 on each side to get...
-10 = b There fore we have a y-intercept of -10 and a given slope of 2 giving us an equation in Slope-Intercept form of
y=2x-10
The other form given in the other solutions, (y-y1)=m(x-x1) is actually called the Point-Slope form of a line and is derived from the slope-intercept form. Using this form, we can plug in the same coordinates given for x1 (3) and y1 (-4), and the slope for m (2).
(y--4)=2(x-3)
y+4=2x-6 subtract 4 from each side...
y=2x-10...the same solution as above.
The standard equation of a straight line with a slope m and passing through a point x1 and y1 is:
y-y1=m(x-x1) (1)
Given m=2, (x1, y1) = (3, -4).
Therefore, substitute th value of m and (x1 , y1) in (1) to get the required equation:
y- (-4) = 2(x-3).
Simplify: y+4=2x-6
or y=2x-6-4
y=2x-10 is the slope and y intercept form
Or 2x-y-10 =0 which is the standard ax+by+c=0 form of the straight line.
Hope this helps.
Let us say the equation of the line is:
y = ax + b ... (1)
Now since slope is equal to 2, the value of a = 2.
Therefore the equation (1) becomes:
y = 2x + b ... (2)
Since the line passes through the point (3, -4) substituting the values of x and y in the above equation we get:
-4 = 2*3 + b = 6 + b
Therefore: b = -4 -6 = -10
Substituting this value of b in equation (2) the equation of the line becomes:
y = 2x - 10 .... Answer.
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