Question

Find the equation of the line that passes through (9,-4) and (-1,-8).

Answer 1

Answer:

$y = \frac{2}{5} x - 7 \frac{3}{5}$

Step-by-step explanation:

Slope-intercept form

y= mx +c, where m is the gradient and c is the y-intercept.

$\boxed{gradient = \frac{y1 - y2}{x1 - x2} }$

Gradient

$= \frac{ - 4 - ( - 8)}{9 - ( - 1)}$

$= \frac{ - 4 + 8}{9 + 1}$

$= \frac{4}{10}$

$= \frac{2}{5}$

Substitute the value of the gradient into the equation:

$y = \frac{2}{5} x + c$

To find the value of the y-intercept, substitute a pair of coordinates.

When x= -1, y= -8,

$- 8 = \frac{2}{5} ( - 1) + c$

$- 8 = - \frac{2}{5} + c$

$c = - 8 + \frac{2}{5}$

$c = - 7 \frac{3}{5}$

Thus the equation of the line is $y = \frac{2}{5} x - 7 \frac{3}{5}$.