Math Problem Equation

Question

Find the equation for the line that passes through the points (8,−2)(8,-2) and (−4,5)(-4,5). Give your answer in point-slope form. You do not need to simplify.

Answer 1

Slope = rise/run = (5 - (-2))/-4 - 8) = 7/-12 or - 7/12.

Point-slope form for 1st point is y - (-2)) = -7/12(x - 8) -> y + 2 = -7/12(x - 8)

Form for 2nd point is y - 5 = -7/12(x - (-4)) -> y - 5 = -7/12(x + 4)

Answer 2

Start with two-point form

(y + 2) / (x - 8) = (5 + 2) / (-4 - 8)

Answer 3

(8,-2) and (-4,5) have a line through them with slope = -7/12 = (y+2)/(x-8)

y+2 = (-7/12)(x-8) in point slope form

or

y-5 = (-7/12)(x+4) using the other point

cross multiply on the 1st equation

12y +24 = -7x +56

12y = -7x +56 -24

12y =- 7x +32

y = (-7/12)x + 8/3 in slope intercept form, where -7/12 = slope and 8/3 = y intercept

-2 = (-7/12)(8) +8/3 = -14/3 +8/3 = -6/3=-2

or 7x+12y = 32 in standard form

or 7x+12y-32=0 in general form