Question

question
use technology to find points and graph the line $-4y = -2x + 8$, following the instructions below.
done plotting points
plot at least two points that fit on the axes below. click a point to delete it.
graph axes here

Explanation:

Step1: Simplify the equation

First, we can simplify the given equation \(-4y = -2x + 8\) by dividing both sides by \(-4\) to get it in slope - intercept form (\(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept).

\[

$$\begin{align*} y&=\frac{-2x + 8}{-4}\\ y&=\frac{-2x}{-4}+\frac{8}{-4}\\ y&=\frac{1}{2}x-2 \end{align*}$$

\]

Step2: Find the y - intercept point

The y - intercept occurs when \(x = 0\). Substitute \(x = 0\) into the equation \(y=\frac{1}{2}x-2\).

\[
y=\frac{1}{2}(0)-2=-2
\]
So, one point on the line is \((0,-2)\).

Step3: Find another point (using x - value)

Let's choose \(x = 4\) (we can choose any value for \(x\), choosing \(x = 4\) makes the calculation of \(y\) easy since \(\frac{1}{2}\times4 = 2\)). Substitute \(x = 4\) into the equation \(y=\frac{1}{2}x-2\).

\[
y=\frac{1}{2}(4)-2=2 - 2=0
\]
So, another point on the line is \((4,0)\).

Answer:

Two points on the line \(-4y=-2x + 8\) (or \(y=\frac{1}{2}x - 2\)) are \((0,-2)\) and \((4,0)\) (we can also use other points. For example, if \(x = 2\), then \(y=\frac{1}{2}(2)-2=1 - 2=-1\), so \((2,-1)\) is also a valid point). To graph the line, we can plot the points \((0,-2)\) and \((4,0)\) (or other pairs of points we find) and then draw a straight line through them.