Question

What is an equation of the line that passes through the points (-4, 2) and (-8, -3)? ​

Answer 1

Answer:

y = 5/4x + 7

Step-by-step explanation:

Given points (-4, 2) and (-8, -3):

Let (x1, y1) = (-4, 2)

(x2, y2) = (-8, -3)

Use these points to solve for the slope of the line:

$m = \frac{y2 - y1}{x2 - x1} = \frac{-3 - 2}{- 8 - (-4)} = \frac{-5}{-4} = \frac{5}{4}$

Therefore, the slope of the line is: m = 5/4.

Next, we must determine the y-intercept. In order to do so, we can use the point-slope form and plug in the values of (-4, 2) into the equation as (x1, y1):

y - y1 = m(x - x1)

$y - 2 = \frac{5}{4}(x - (-4))$

$y - 2 = \frac{5}{4}(x + 4)$

$y - 2 = \frac{5}{4}x + 5$

Add 2 on both sides of the equation:

$y - 2 + 2 = \frac{5}{4}x + 5 + 2$

y = 5/4x + 7

Therefore, the equation of the line is: y = 5/4x + 7 where the slope (m) is 5/4, and the y-intercept (b) is 7.