point slope

Question

Write an equation in point slope form and slope intercept form for the line that passed through (-5,-10) and (-9,8).

Answer 1

Hi, Lisa.

 

Remember that the point-slope form of a linear equation with point (x₁, y₁) and slope m:

 

y - y₁ = m(x - x₁)  and the slope-intercept form: y = mx + b.

 

Therefore, using the points (-5, -10), and (-9, 8), we find the slope: (8 - (-10))/(-9 - (-5)) = 18/-4.

 

So m=-9/2.  Using one of the points:  y - 8 = (-9/2)/(x - (-9)) or:   y - 8 = (-9/2)(x + 9)

 

To convert to slope intercept, add 8 to both sides and distribute the -9/2.

 

Thus: y = (-9/2)x - 81/2 + 8 ==>  or y = (-9/2)x - 65/2

 

I hope this helps.

Answer 2

The slope of the line is (8 - (-10))/(-9 - (-5)) = 18/(-4) = -4.5

 

Point-slope form:  y - 8 = -4.5(x - (-9))

                            y - 8 = -4.5(x + 9)

 

Solving the point-slope form for y, we obtain the slope-intercept form:

     y - 8 = -4.5x - 40.5

         y = -4.5x - 32.5