The equation y=3/4x−5

Question

 describes the relationship between quantities x and y on the graph below.

Are the quantities in a proportional relationship?

(1 point)
Responses

Yes, because the graph of the equation is a straight line.
Yes, because the graph of the equation is a straight line.

Yes, because the graph of the equation passes through the origin.
Yes, because the graph of the equation passes through the origin.

No, because the graph of the equation is not a straight line.
No, because the graph of the equation is not a straight line.

No, because the graph of the equation does not pass through the origin and the ratio of y/x is not equivalent for each point on the line.
No, because the graph of the equation does not pass through the origin and the ratio of y/x is not equivalent for each point on the line.
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Answer 1

The correct response is:

No, because the graph of the equation does not pass through the origin and the ratio of y/x is not equivalent for each point on the line.

In a proportional relationship, the graph is a straight line that passes through the origin (0,0), and the ratio of \(y/x\) must be constant for all points. In this case, the equation \(y = \frac{3}{4}x - 5\) indicates that the line has a y-intercept of -5, which means it does not pass through the origin, thus indicating that the relationship is not proportional.