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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

1 answer

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

  1. The equation \( y = 15x \) implies that the slope \( m = 15 \), meaning for every 1 unit increase in \( x \), \( y \) should increase by 15 units.

  2. The two plotted points are \( (0, 0) \) and \( (5, 1) \).

  3. Checking the slope between the points \( (0, 0) \) and \( (5, 1) \):

    • The change in \( y \) (rise) is \( 1 - 0 = 1 \).
    • The change in \( x \) (run) is \( 5 - 0 = 5 \).
    • Therefore, the slope \( m = \frac{1}{5} \).

Since the slope \( \frac{1}{5} \) does not equal 15, the line does not match the equation \( y = 15x \).

  1. Additionally, the point \( (1, 5) \) should satisfy the equation \( y = 15x \):
    • Substituting \( x = 1 \) into \( y = 15x \) gives \( y = 15(1) = 15 \), which does not match \( (1, 5) \).

Given this analysis, the correct response is:

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