Question

multiple choice 5 points which represents the graph of the equation 2x - 4y = 8 ?

Explanation:

Step1: Rewrite the equation in slope - intercept form

The given equation is \(2x - 4y=8\). We want to write it in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
First, isolate \(y\):

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So the slope \(m=\frac{1}{2}\) and the y - intercept \(b = - 2\).

Step2: Analyze the graph

We can also find the x - intercept and y - intercept from the original equation.

• For the y - intercept, set \(x = 0\) in \(2x-4y = 8\):

\(2(0)-4y=8\Rightarrow-4y = 8\Rightarrow y=-2\). So the y - intercept is \((0,-2)\).

• For the x - intercept, set \(y = 0\) in \(2x-4y = 8\):

\(2x-4(0)=8\Rightarrow2x=8\Rightarrow x = 4\). So the x - intercept is \((4,0)\).

Now, looking at the graph, we can check if it passes through \((0,-2)\) and \((4,0)\) (or has a slope of \(\frac{1}{2}\)). The line in the given graph has a y - intercept of \(- 2\) (crosses the y - axis at \((0,-2)\)) and an x - intercept that we can calculate from the slope - intercept form or the original equation. Since the equation \(y=\frac{1}{2}x - 2\) has a positive slope (\(\frac{1}{2}\)) and y - intercept \(-2\), and the given graph matches these characteristics (passes through \((0,-2)\) and has a positive slope), this graph represents the equation \(2x-4y = 8\).

Answer:

The graph shown (the one with y - intercept at \((0, - 2)\) and x - intercept at \((4,0)\) and a positive slope) represents the equation \(2x - 4y=8\).