Question

What is an equation of the line that passes through the points (-6, -2) and (-3, -3)?

Answer 1

Answer:

$y = - \frac{1}{3} x - 4$

Step-by-step explanation:

The equation of a kind can be written in the slope intercept form, y= mx +c, where m is the gradient and c is the y-intercept.

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

$m = \frac{ - 2 - ( - 3)}{ - 6 - ( - 3)}$

$m = \frac{ - 2 + 3}{ - 6 + 3}$

$m = \frac{ 1}{ - 3}$

Substitute the value of m into the equation:

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

To find the value of c, substitute a pair of coordinates.

When x= -3, y= -3,

$- 3 = - \frac{1}{3} ( - 3) + c$

$- 3 = 1 + c$

c= -3 -1

c= -4

∴ The equation of the line is $y = - \frac{1}{3} x -4$.