Question

graph the line.
-8x + 4y = 16
use the graphing tool to graph the equation.

Explanation:

Step1: Rewrite in 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.
We start with the equation $- 8x+4y = 16$.
First, we isolate $y$:
Add $8x$ to both sides of the equation: $4y=8x + 16$.
Then divide each term by 4: $y=\frac{8x}{4}+\frac{16}{4}$, which simplifies to $y = 2x+4$.

Step2: Identify the y - intercept and slope

For the equation $y = 2x + 4$, the y - intercept $b = 4$. This means the line crosses the y - axis at the point $(0,4)$.
The slope $m = 2$, which can be written as $\frac{2}{1}$. The slope represents the rise over run, so from the point $(0,4)$, we can go up 2 units and then right 1 unit to get another point on the line (for example, $(1,6)$), or down 2 units and left 1 unit (for example, $(- 1,2)$).

Step3: Graph the line

Plot the y - intercept $(0,4)$ on the coordinate plane. Then use the slope to find another point (or points) on the line. Draw a straight line through these points.

Answer:

To graph the line $-8x + 4y=16$ (or $y = 2x + 4$), plot the y - intercept $(0,4)$ and use the slope $m = 2$ (rise 2, run 1) to find additional points, then draw a line through them.