Use the image to answer the question.

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 .

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
.
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 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

Answer 1

To determine whether the graph is correct for the equation \( y = 15x \), we need to analyze the points given:

1. The points on the graph are \( (0, 0) \) and \( (5, 1) \).

2. First, check if the point \( (0, 0) \) satisfies the equation \( y = 15x \):

   • For \( x = 0 \): \[ y = 15(0) = 0 \] Thus, \( (0, 0) \) does satisfy the equation.

3. Now, check the point \( (5, 1) \) with the equation \( y = 15x \):

   • For \( x = 5 \): \[ y = 15(5) = 75 \] The point \( (5, 1) \) does not satisfy the equation since \( 1 \neq 75 \).

4. Additionally, we can calculate the slope (\( m \)) based on the two given points:

   • Rise = \( 1 - 0 = 1 \)
   • Run = \( 5 - 0 = 5 \)
   • Thus, the slope \( m = \frac{\text{rise}}{\text{run}} = \frac{1}{5} \).

Since the slope derived from the points is \( \frac{1}{5} \), which does not match the slope of \( 15 \) in the equation \( y = 15x \), we conclude that the graph is not correctly representing the equation.

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