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.

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

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
.

GPT-4o mini · Answer

To determine if the line joining the points (0, 0) and (5, 1) represents the equation \( y = 15x \), we first need to find the slope of the line formed by these two points.

The slope \( m \) is calculated as: \[ m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1} \] where \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (5, 1)\).

Plugging in the values: \[ m = \frac{1 - 0}{5 - 0} = \frac{1}{5} \]

Now, let's analyze the equation \( y = 15x \). This equation has a slope of 15, which is significantly different from the slope we calculated (\(\frac{1}{5}\)).

Given these findings, the correct answer is: No, it is not the correct graph because the slope \( m = \frac{\text{rise}}{\text{run}} = \frac{1}{5} \) ≠ 15.