Write an equation for the line that passes through the points (-5, 4) and (3, -2) .

Answer 1

Given:

P1: (-5, 4)

P2: (3, -2)

Find:

The equation for the line that passes thru P1 & P2

Solution:

y = mx + b

Will be the equation to arrive to at the very end, but we need m & b, the slope and the y-intercept

m = ( y₂ - y₁ ) / ( x₂ - x₁ ) = ( -2 - 4 ) / ( 3 - ( -5 ) ) = -6 / 8

∴ m = - 3/4

Using either P1 or P2, plug in one of their respective x- and y-values into:

y = -3/4 x + b

I'll do (3, -2):

-2 = -3/4 ( 3 ) + b

-2 = -9/4 + b

-8 = -9 + 4b

1 = 4b

∴ b = 1/4

∴ y = -3/4 x + 1/4 is the equation of the line that passes thru both points (-5, 4) and (3, -2)

I hope this helps! Message me in the comments if you have any questions, comments, or concerns!