Question

score: 0/2 penalty: none question what is an equation of the line that passes through the points (0, -8) and (-8, 2)? answer you have up to 6 questions left to raise your score.

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1,y_1)=(0, - 8)\) and \((x_2,y_2)=(-8,2)\). So, \(m=\frac{2-(-8)}{-8 - 0}=\frac{2 + 8}{-8}=\frac{10}{-8}=-\frac{5}{4}\).

Step2: Use the y - intercept form

The y - intercept form of a line is \(y=mx + b\), where \(b\) is the y - intercept. The point \((0,-8)\) is the y - intercept (since \(x = 0\)), so \(b=-8\). Substitute \(m =-\frac{5}{4}\) and \(b=-8\) into the equation: \(y=-\frac{5}{4}x-8\). We can also convert it to standard form. Multiply both sides by 4: \(4y=-5x - 32\), then \(5x+4y=-32\). But the slope - intercept form is also acceptable.

Answer:

\(y =-\frac{5}{4}x-8\) (or \(5x + 4y=-32\))