Multiple Choice
Which equation has a graph parallel to the graph of 9x + 3y = –22 ?
(1 point)
Responses
y = 3x – 22
y = 3 x – 22
y = –3x + 8
y = – 3 x + 8
y = one-thirdx + 12
y = Image with alt text: one-third x + 12
y = –one-thirdx – 2
y = –one-thirdx – 2
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To determine which equation has a graph parallel to the graph of 9x + 3y = -22, we need to find an equation in the form y = mx + b, where m represents the slope of the line.
To do this, let's rewrite the given equation, 9x + 3y = -22, in the slope-intercept form.
9x + 3y = -22
3y = -9x - 22
y = (-9/3)x - 22/3
y = -3x - 22/3
Now we can observe that the slope of this line is -3.
Next, we need to look at the answer choices and find an equation that has the same slope (-3) to be parallel to the given line.
Among the answer choices:
1) y = 3x - 22: The slope of this equation is 3, which is not parallel to the slope of the given line (-3). Eliminate this choice.
2) y = -3x + 8: This equation has the same slope, -3, as the given line. It is parallel to the given graph. Keep this choice for now.
3) y = (1/3)x + 12: The slope of this equation is 1/3, which is not parallel to the slope of the given line (-3). Eliminate this choice.
4) y = (-1/3)x - 2: The slope of this equation is -1/3, which is not parallel to the slope of the given line (-3). Eliminate this choice.
Therefore, the equation that has a graph parallel to the graph of 9x + 3y = -22 is y = -3x + 8.