Question

step 4: sketch the graph 1. draw a coordinate plane. 2. plot the points \\((4, 0)\\) and \\((0, -2)\\). 3. draw a straight line passing through both points.

Explanation:

Identify the given equation

We are given the linear equation shown on the graph:

$$2x - 4y = 8$$

Solve for y in terms of x

To find the slope-intercept form \(y = mx + b\), we isolate \(y\):

$$-4y = -2x + 8$$

Divide both sides by \(-4\):

$$y = \frac{-2}{-4}x + \frac{8}{-4}$$

$$y = \frac{1}{2}x - 2$$

Verify with graph features

The equation \(y = \frac{1}{2}x - 2\) has:

• A \(y\)-intercept at \((0, -2)\).
• An \(x\)-intercept at \((4, 0)\).
• A slope of \(m = \frac{1}{2}\).

These values perfectly match the plotted line and labels in the image.

Answer:

Line: \(y =\) <blank>\(\frac{1}{2}x - 2\)</blank>