Question

1. graph the line through (0,9) with a slope of -2/3.

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given the point $(0,9)$, the y - intercept $b = 9$ and the slope $m=-\frac{2}{3}$. So the equation of the line is $y=-\frac{2}{3}x + 9$.

Step2: Find another point

Use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Starting from the point $(x_1,y_1)=(0,9)$ and $m =-\frac{2}{3}$, if we let $x_2=3$, then $-\frac{2}{3}=\frac{y_2 - 9}{3 - 0}$. Cross - multiply: $- 2=y_2 - 9$. Solve for $y_2$: $y_2=7$. So another point on the line is $(3,7)$.

Step3: Graph the line

Plot the points $(0,9)$ and $(3,7)$ on the coordinate plane and draw a straight line passing through them.

Answer:

Graph the line by plotting the points $(0,9)$ and $(3,7)$ and drawing a straight - line through them.