Question

Which statement about the graph is true?

On a coordinate plane, a line goes through points (0, 2), (2, 3), (4, 4), (6, 5).
A. The graph shows a proportional relationship because it is a line, and the difference between each point is the same.
B. The graph shows a proportional relationship because it is a line, and each x-value is a multiple of 2.
C. The graph does not show a proportional relationship because each point written as a ratio gives a different value.
D. The graph does not show a proportional relationship because a line that increases by 1 in the y-value cannot have a constant of proportionality.

Answer 1

a

Explanation:

Answer 2

C. The graph does not show a proportional relationship because each point written as a ratio gives a different value.

Explanation:

The equation of a line in slope-intercept form is

y = mx + b

Where m is the slope and b is the y-intercept.

Not all lines represent proportional relationships. The condition for a line to be a proportional function is that b=0, i.e., the y-intercept is the origin.

The graph shown in the figure has a y-intercept of 2, thus the line is not a proportional relationship.

If the equation of the line is proportional (b=0), then:

y = mx

Or:

y/x = m

The ratio between each value of y and x must be constant.

This is not the case, because

3/2, 4/4, 6/5 result in different values and 2/0 doesn't even exist. Thus the correct answer is:

C. The graph does not show a proportional relationship because each point written as a ratio gives a different value.