Question

2x + 4y = 8\
2y = 3x - 12\
choose the correct line to graph: line 1 is line ab. line 2 is line cd\
(chart and selection buttons as described)

Explanation:

Step1: Convert equations to slope - intercept form

For the first equation \(2x + 4y=8\), solve for \(y\):
Subtract \(2x\) from both sides: \(4y=-2x + 8\)
Divide by 4: \(y=-\frac{1}{2}x + 2\)

For the second equation \(2y = 3x-12\), solve for \(y\):
Divide by 2: \(y=\frac{3}{2}x-6\)

Step2: Analyze the lines based on slope - intercept form

• The line \(y =-\frac{1}{2}x + 2\) has a \(y\) - intercept of \(2\) (when \(x = 0\), \(y=2\)) and a slope of \(-\frac{1}{2}\) (negative slope, decreasing line). Looking at the graph, the line passing through points \(A(0,2)\) and \(B(1,1)\) (since when \(x = 1\), \(y=-\frac{1}{2}(1)+2=\frac{3}{2}\)? Wait, actually, when \(x = 0\), \(y = 2\) (point \(A\)), when \(x = 2\), \(y=-\frac{1}{2}(2)+2 = 1\) (point \(B\)). So this line is Line AB.
• The line \(y=\frac{3}{2}x - 6\) has a \(y\) - intercept of \(-6\) (when \(x = 0\), \(y=-6\), point \(C\)) and a slope of \(\frac{3}{2}\) (positive slope, increasing line). When \(x = 2\), \(y=\frac{3}{2}(2)-6=3 - 6=-3\)? Wait, when \(x = 1\), \(y=\frac{3}{2}(1)-6=\frac{3 - 12}{2}=-\frac{9}{2}=-4.5\)? Wait, the point \(D\) seems to be at \(x = 1\), \(y=-5\)? Wait, maybe better to check the \(y\) - intercepts. The line with \(y\) - intercept \(2\) is Line AB (since point \(A\) is at \((0,2)\)) and the line with \(y\) - intercept \(-6\) is Line CD (point \(C\) is at \((0,-6)\)).

So, the equation \(2x + 4y = 8\) (which is \(y=-\frac{1}{2}x + 2\)) corresponds to Line AB, and the equation \(2y=3x - 12\) (which is \(y=\frac{3}{2}x-6\)) corresponds to Line CD.

If we are to graph \(2x + 4y = 8\), we choose Line AB. If we are to graph \(2y=3x - 12\), we choose Line CD.

Assuming we need to match the equations to the lines:

• For \(2x + 4y = 8\) ( \(y=-\frac{1}{2}x + 2\)): Line AB (since it has \(y\) - intercept \(2\) and negative slope)
• For \(2y=3x - 12\) ( \(y=\frac{3}{2}x-6\)): Line CD (since it has \(y\) - intercept \(-6\) and positive slope)

Answer:

If the equation to graph is \(2x + 4y = 8\), the correct line is Line AB. If the equation to graph is \(2y=3x - 12\), the correct line is Line CD.

(If we assume the question is to match \(2x + 4y = 8\) to a line, the answer is Line AB; if it's \(2y = 3x-12\), the answer is Line CD. Since the problem says "Choose the correct line to graph" without specifying the equation, but from the equations given, we can conclude:

For \(2x + 4y = 8\): Line AB

For \(2y=3x - 12\): Line CD)