Question

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 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= 1/5 x?

Answer 1

Yes, it is the correct graph because the slope =5/1.
No, it is not the correct graph because the slope m=riserun=1/5.

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

No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y=1/5x

Answer 2

To determine if the line connecting the points (0, 0) and (5, 1) is the correct graph of the equation \( y = \frac{1}{5}x \), we can check whether these points satisfy the equation.

1. **Check Point (0, 0)**:
- Substitute \( x = 0 \) into the equation:
\[
y = \frac{1}{5}(0) = 0
\]
- This point lies on the line.

2. **Check Point (5, 1)**:
- Substitute \( x = 5 \) into the equation:
\[
y = \frac{1}{5}(5) = 1
\]
- This point also lies on the line.

Since both points (0, 0) and (5, 1) satisfy the equation \( y = \frac{1}{5}x \), the line plotted between these points correctly represents the equation. The line will continue to extend in both directions as per the definition of a line.

Thus, yes, this is the correct graph of the equation \( y = \frac{1}{5}x \).

Answer 3

The correct conclusion regarding the graph of the equation \( y = \frac{1}{5}x \) and the points (0, 0) and (5, 1) is:

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

### Explanation:
1. The slope \( m \) calculated from the points (0, 0) and (5, 1) is:
\[
m = \frac{1 - 0}{5 - 0} = \frac{1}{5}.
\]

2. Both points satisfy the equation \( y = \frac{1}{5}x \):
- For \( (0, 0) \): \( y = \frac{1}{5}(0) = 0 \)
- For \( (5, 1) \): \( y = \frac{1}{5}(5) = 1 \)

3. The ordered pair (1, 5) is not relevant here since it does not pertain to the two points provided; in fact, (1, 5) does not satisfy the equation \( y = \frac{1}{5}x \) as:
- For \( (1, 5) \): \( y = \frac{1}{5}(1) = 0.2 \) which is not equal to 5.

Therefore, the correct statement is that it is indeed the correct graph as both the slope and the points are consistent with the equation \( y = \frac{1}{5}x \).