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

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

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 ordered pair (0, 0)
satisfies the equation and the slope

Answer 1

To determine whether the line connecting the points (0, 0) and (5, 1) represents the equation \( y = 15x \), we need to analyze the points and calculate the slope.

1. Calculate the slope of the line:

   • The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
   • Using the points (0, 0) and (5, 1): \[ m = \frac{1 - 0}{5 - 0} = \frac{1}{5} \]

2. Compare slopes:

   • The slope of the line \( y = 15x \) is 15, while the calculated slope from the points (0, 0) and (5, 1) is \( \frac{1}{5} \).

Since the computed slope \( \frac{1}{5} \) does not equal the slope of the line defined by \( y = 15x \), it confirms that the plotted points do not satisfy the equation \( y = 15x \).

Based on this analysis, the correct response is:

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