Question

describe the key features of the graph. -4x + 8y = 16

Explanation:

Step1: Rewrite in slope - intercept form

First, rewrite the equation $-4x + 8y=16$ in the form $y = mx + b$. Add $4x$ to both sides: $8y=4x + 16$. Then divide each term by 8: $y=\frac{4}{8}x+\frac{16}{8}$, which simplifies to $y=\frac{1}{2}x + 2$.

Step2: Identify the slope and y - intercept

The slope $m=\frac{1}{2}$, which means for every 2 units of increase in $x$, $y$ increases by 1 unit. The y - intercept $b = 2$, which is the point $(0,2)$ where the line crosses the y - axis.

Step3: Find the x - intercept

Set $y = 0$ in the original equation $-4x+8y = 16$. We get $-4x=16$, so $x=-4$. The x - intercept is the point $(-4,0)$.

Answer:

The key features of the graph of the line $-4x + 8y=16$ are: slope $m=\frac{1}{2}$, y - intercept at the point $(0,2)$ and x - intercept at the point $(-4,0)$.