What is the equation of a line that passes through the point (3,-4) and has a slope of 2?

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kjcdb8er's profile pic

kjcdb8er | Teacher | (Level 1) Associate Educator

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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 the information from your question, and let's see what we get:

-4 = 2*3 + b   or   b = -4 - 2*3 = -10. So m = 2, and b = -10, thus the equation for the line that passes through the point (3,-4) is:

y = 2x - 10

 

You could also use the slope intercept form of the equation for a line for a point (x1,y1), which is:

y - y1 = m(x - x1) --> y - -4 = 2(x - 3) or,

y + 4 = 2x - 6

y = 2x - 6 - 4

y = 2x - 10

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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(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

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neela | High School Teacher | (Level 3) Valedictorian

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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.

 

Top Answer

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

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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.

acompanioninthetardis's profile pic

acompanioninthetardis | Student, Undergraduate | (Level 1) Valedictorian

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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

itssnigdha's profile pic

itssnigdha | Student, Grade 11 | (Level 2) Honors

Posted on

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

jdetringo's profile pic

jdetringo | Middle School Teacher | eNotes Newbie

Posted on

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.

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