graph the line that passes through the points (-5, -2) and (5, -8) and determine the equation of the line.

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-5,-2)$ and $(x_2,y_2)=(5,-8)$. Then $m=\frac{-8 - (-2)}{5-(-5)}=\frac{-8 + 2}{5 + 5}=\frac{-6}{10}=-\frac{3}{5}$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ and then convert to slope - intercept form $y=mx + b$. Let's use the point $(-5,-2)$ and $m =-\frac{3}{5}$. $y-(-2)=-\frac{3}{5}(x - (-5))$ $y + 2=-\frac{3}{5}(x + 5)$ $y+2=-\frac{3}{5}x-3$ $y=-\frac{3}{5}x-5$. So the y - intercept $b=-5$.

Step3: Graph the line

Plot the two points $(-5,-2)$ and $(5,-8)$ on the coordinate plane. Then draw a straight line passing through them. The y - intercept is at the point $(0,-5)$.

Answer:

The equation of the line is $y =-\frac{3}{5}x-5$. To graph, plot the points $(-5,-2)$, $(5,-8)$ and $(0,-5)$ and draw a straight line through them.