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 with x and y axes from -10 to 10)

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).

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Step2: Find the y - intercept point

The y - intercept occurs when \(x = 0\). Substitute \(x = 0\) into the equation \(y=\frac{1}{2}x-2\).
When \(x = 0\), \(y=\frac{1}{2}(0)-2=-2\). So one point on the line is \((0,-2)\).

Step3: Find another point

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

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So another point on the line is \((4,0)\). We can also find other points. For example, if \(x = 2\), then \(y=\frac{1}{2}(2)-2=1 - 2=-1\), so the point is \((2,-1)\).

To graph the line, we can plot the points \((0,-2)\) and \((4,0)\) (or other points we found) on the coordinate plane and then draw a straight line through them.

Answer:

Two points on the line \(-4y=-2x + 8\) (or \(y=\frac{1}{2}x - 2\)) are \((0,-2)\) and \((4,0)\) (other valid points can also be used, like \((2,-1)\) etc.). When graphing, plot these points on the given coordinate system and draw a line through them.