Question

1. graph the following using the slope and y-intercept. show all your calculations work.

2x - 3y = 9

Explanation:

Step1: Convert to slope - intercept form ($y = mx + b$)

We start with the equation $2x - 3y=9$. We want to solve for $y$. First, subtract $2x$ from both sides:
$- 3y=-2x + 9$
Then, divide every term by $-3$:
$y=\frac{-2x}{-3}+\frac{9}{-3}$
Simplify the fractions:
$y = \frac{2}{3}x-3$

Step2: Identify slope and y - intercept

In the slope - intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
For the equation $y=\frac{2}{3}x - 3$, the slope $m=\frac{2}{3}$ and the y - intercept $b=- 3$. The y - intercept is the point where $x = 0$, so the point is $(0,-3)$.

Step3: Find another point using the slope

The slope $\frac{2}{3}$ means that for a run (change in $x$) of $3$, the rise (change in $y$) is $2$. Starting from the y - intercept $(0,-3)$, if we add $3$ to the $x$ - coordinate (run = 3) and add $2$ to the $y$ - coordinate (rise = 2), we get the point $(0 + 3,-3+2)=(3,-1)$.

Step4: Graph the line

Plot the points $(0,-3)$ and $(3,-1)$ on the coordinate plane. Then, draw a straight line through these two points. This line represents the equation $2x-3y = 9$.

Answer:

The equation in slope - intercept form is $y=\frac{2}{3}x - 3$, with slope $\frac{2}{3}$ and y - intercept at $(0,-3)$. The line can be graphed by plotting the points $(0,-3)$ and $(3,-1)$ and drawing a line through them.