Question

What is the equation of the lines that passes through the points (-2, -3) and (4, -5)?
A) y= -1/3x-3
B) y= -4x-11/3
C) y= 4x+3
D) y= -1/3x-11/3

Answer 1

Since all the options are in the slope intercept form, we find the equation using the formula,

$y = mx + c$
We can find m, the slope using the formula,

$m = \frac{ change \: in \: y }{change \: in \: x}$
$m = \frac{ - 5 - - 3}{4 - - 2}$
$m = \frac{ - 2}{6} = - \frac{1}{3}$

On substitution,

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

We use any of the points, say (-2,-3) to determine the value of c.

$- 3 = - \frac{1}{3} ( - 2) + c$
$c = - \frac{11}{3}$

The equation is therefore,

$y = - \frac{1}{3} x - \frac{11}{3}$

The correct answer is D.