graph the line that passes through the points (-8,6) and (-6,3) and determine the equation of the line.

Explanation:

Step1: Calculate the slope

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

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-8,6)$ and $m =-\frac{3}{2}$, we have $y - 6=-\frac{3}{2}(x + 8)$.

Step3: Simplify to slope - intercept form

Expand the right side: $y-6=-\frac{3}{2}x-12$. Add 6 to both sides: $y=-\frac{3}{2}x - 6$.

Answer:

The equation of the line is $y =-\frac{3}{2}x-6$. To graph, plot the points $(-8,6)$ and $(-6,3)$ and draw a straight line through them.