Question

example 5 graph 12x - 3y = 18 1. rewrite the equation in slope - intercept form 2. plot the y - intercept. 3. the slope is rise/run = □. from (0,□), move up □ units and right □ unit. plot the point (□,□) 4. describe the key features of the graph.

Explanation:

Step1: Rewrite in slope - intercept form

The slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $12x-3y = 18$, solve for $y$:
\[

$$\begin{align*} -3y&=-12x + 18\\ y& = 4x-6 \end{align*}$$

\]

Step2: Find the y - intercept

In the equation $y = 4x - 6$, when $x = 0$, $y=-6$. So the y - intercept is the point $(0,-6)$.

Step3: Find the slope

The slope $m = 4=\frac{4}{1}$. From the point $(0,-6)$, to find another point, we use the slope. The slope $\frac{rise}{run}=4$, which means from $(0,-6)$ we move up 4 units and right 1 unit. The new point is $(1,-2)$.

Step4: Describe key features

The key features are: y - intercept at $(0,-6)$, slope $m = 4$, and we can plot points like $(0,-6)$ and $(1,-2)$ to graph the line.

Answer:

1. $y = 4x-6$
2. $(0,-6)$
3. $\frac{4}{1}$, from $(0,-6)$, move up 4 units and right 1 unit
4. y - intercept at $(0,-6)$, slope $m = 4$, points $(0,-6)$ and $(1,-2)$ can be used to graph