graph the line that passes through the points (9, 8) and (6, 4) and determine the equation of the line.

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(9,8)$ and $(x_2,y_2)=(6,4)$. So $m=\frac{4 - 8}{6 - 9}=\frac{-4}{-3}=\frac{4}{3}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Let's use the point $(6,4)$ and $m = \frac{4}{3}$. Then $y - 4=\frac{4}{3}(x - 6)$.

Step3: Simplify to slope - intercept form

Expand the right - hand side: $y-4=\frac{4}{3}x-8$. Add 4 to both sides to get $y=\frac{4}{3}x - 4$.

To graph the line:

1. Plot the two given points $(9,8)$ and $(6,4)$ on the coordinate plane.
2. Use the slope $\frac{4}{3}$ (rise 4 units and run 3 units) to find other points on the line. Starting from either of the given points, for example, from $(6,4)$, if we move 3 units to the right (increase $x$ by 3) and 4 units up (increase $y$ by 4), we get another point on the line. Then draw a straight line passing through these points.

Answer:

The equation of the line is $y=\frac{4}{3}x - 4$