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=1/5x
?

(1 point)
Responses

Yes, it is the correct graph because the ordered pair (0, 0)
satisfies the equation and the slope m=riserun=1/5
.
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=1/5
.
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 =5/1
.
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=1/5x

1 answer

To determine if the given graph represents the equation \( y = \frac{1}{5}x \), let's evaluate the points and the slope.

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

  2. The ordered pair \( (0, 0) \) does satisfy the equation because if \( x = 0 \), then \( y = \frac{1}{5}(0) = 0 \).

  3. Now let's check if the ordered pair \( (5, 1) \) satisfies the equation: \[ y = \frac{1}{5}(5) = 1. \] So, \( (5, 1) \) also satisfies the equation.

  4. Next, calculate the slope \( m \) between the two points: \[ m = \frac{\text{rise}}{\text{run}} = \frac{1 - 0}{5 - 0} = \frac{1}{5}. \] This is the same as the slope given in the equation.

Since both points satisfy the equation \( y = \frac{1}{5}x \) and the calculated slope matches, the response to the question is:

Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope \( m = \frac{1}{5} \).