graph the line that passes through the points (9, -1) and (6, 1) 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 $(x_1,y_1)=(9,-1)$ and $(x_2,y_2)=(6,1)$. Then $m=\frac{1-(-1)}{6 - 9}=\frac{2}{-3}=-\frac{2}{3}$.

Step2: Use point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(6,1)$ and $m =-\frac{2}{3}$, we have $y - 1=-\frac{2}{3}(x - 6)$.

Step3: Simplify to slope - intercept form

Expand the right side: $y - 1=-\frac{2}{3}x+4$. Add 1 to both sides to get $y=-\frac{2}{3}x + 5$. To graph, plot the two points $(9,-1)$ and $(6,1)$ and draw a straight line through them.

Answer:

The equation of the line is $y =-\frac{2}{3}x+5$