page 15 of 15

Graphing Proportional Relationships Quick Check
5 of 55 of 5 Items

Question
Use the image to answer the question.

A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 5 comma 1 right parenthesis.

Is this the correct graph of the equation y=15x
?

(1 point)
Responses

No, it is not the correct graph because the ordered pair (1, 5)
is not a point on the graph of y=15x
No, it is not the correct graph because the ordered pair left parenthesis 1 comma 5 right parenthesis is not a point on the graph of y equals Start Fraction 1 over 5 End Fraction x

Yes, it is the correct graph because the ordered pair (0, 0)
satisfies the equation and the slope m=riserun=15
.
Yes, it is the correct graph because the ordered pair left parenthesis 0 comma 0 right parenthesis satisfies the equation and the slope m equals Start Fraction rise over run End Fraction equals Start Fraction 1 over 5 End Fraction .

No, it is not the correct graph because the slope m=riserun=15
.
No, it is not the correct graph because the slope m equals Start Fraction rise over run End Fraction equals Start Fraction 1 over 5 End Fraction .

Yes, it is the correct graph because the slope =51
.

1 answer

To determine if the graph represents the equation \( y = 15x \), let's analyze the given points and the information:

  1. The points plotted are \( (0, 0) \) and \( (5, 1) \).
  2. For the equation \( y = 15x \):
    • When \( x = 0 \): \( y = 15(0) = 0 \) (which matches the point (0,0)).
    • When \( x = 5 \): \( y = 15(5) = 75 \) (which does not match the point (5, 1)).

Now checking the alternative expression based on the point \( (5, 1) \):

  • The slope (rise/run) between the points \( (0, 0) \) and \( (5, 1) \) can be calculated:
    • Rise = \( 1 - 0 = 1 \)
    • Run = \( 5 - 0 = 5 \)
    • Slope \( m = \frac{1}{5} \).

This slope suggests a different equation, specifically the equation of a line with a slope of \( \frac{1}{5} \), which is \( y = \frac{1}{5}x \).

Based on the above analysis, the correct response is:

No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of \( y = 15x \).