Question

Find the equation (in terms of x) of the line through the points ( − 1 , − 1 ) and( 4 , − 4 )

Answer 1

Answer:

$y = -\frac{3}{5}x -\frac{8}{5}$

Step-by-step explanation:

Given

$(x_1,y_1) = (-1,-1)$

$(x_2,y_2) = (4,-4)$

Required

Determine the line equation

First, calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{-4 - (-1)}{4 - (-1)}$

$m = \frac{-4 +1}{4 +1}$

$m = \frac{-3}{5}$

$m = -\frac{3}{5}$

The equation is then calculated using:

$y - y_1 = m(x - x_1)$

This gives:

$y - (-1) = -\frac{3}{5}(x - (-1))$

$y + 1 = -\frac{3}{5}(x +1))$

Open bracket

$y + 1 = -\frac{3}{5}x -\frac{3}{5}$

Make y the subject

$y = -\frac{3}{5}x -\frac{3}{5}-1$

$y = -\frac{3}{5}x +\frac{-3-5}{5}$

$y = -\frac{3}{5}x +\frac{-8}{5}$

$y = -\frac{3}{5}x -\frac{8}{5}$