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Graphing Proportional Relationships Quick Check

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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

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 .

Yes, it is the correct graph because the slope =51
.
Yes, it is the correct graph because the slope equals Start Fraction 5 over 1 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 .

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
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1 answer

To determine if the graph corresponds to the equation \( y = 15x \), we need to analyze the given points and the slope:

  1. Ordered Pair Check: The graph includes the point (0, 0). This satisfies any line equation, including \( y = 15x \), since when \( x = 0 \), \( y \) is also \( 0 \).

  2. Slope Calculation: The other point given is (5, 1). The slope \( m \) of the line that passes through the points (0, 0) and (5, 1) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 0}{5 - 0} = \frac{1}{5} \] This means the slope of the line on the graph is \( \frac{1}{5} \).

  3. Comparing Slopes: The slope from the equation \( y = 15x \) is \( 15 \), not \( \frac{1}{5} \). Therefore, the slope calculated from the graph does not match the slope that would be expected from the equation \( y = 15x \).

Based on this analysis, the correct response is:

No, it is not the correct graph because the slope \( m = \frac{1}{5} \).