Question

question what is an equation of the line that passes through the points (6, - 5) and (8, - 6)?

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(6,-5)$ and $(x_2,y_2)=(8,-6)$. Then $m=\frac{-6-(-5)}{8 - 6}=\frac{-6 + 5}{2}=-\frac{1}{2}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(6,-5)$ and $m =-\frac{1}{2}$, we have $y-(-5)=-\frac{1}{2}(x - 6)$.

Step3: Simplify the equation

$y + 5=-\frac{1}{2}x+3$. Then $y=-\frac{1}{2}x-2$.

Answer:

$y =-\frac{1}{2}x-2$