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

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 .

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 accurately represents the equation \( y = 15x \), we need to analyze the slope and the points provided.

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

  1. Check the point (0, 0): This point satisfies the equation \( y = 15x \) because when \( x = 0 \), \( y \) also equals \( 0 \).

  2. Find the slope between the points (0, 0) and (5, 1):

    • The slope \( m \) is calculated as \( m = \frac{\text{rise}}{\text{run}} \).
    • From \( (0, 0) \) to \( (5, 1) \):
      • The rise = \( 1 - 0 = 1 \)
      • The run = \( 5 - 0 = 5 \)
      • Thus, \( m = \frac{1}{5} \).
  3. Compare with the slope of the given equation:

    • The slope of \( y = 15x \) is \( 15 \), significantly different from \( \frac{1}{5} \).

Given that the slope calculated from the points does not match the slope of the equation \( y = 15x \), we conclude that this is not the correct graph for that equation.

Therefore, the appropriate response is:

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