Graphing Equations Quick Check

Question

5 of 55 of 5 Items

Question
Use the image to answer the question.
A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma 3 right parenthesis, and left parenthesis 3 comma 2 right parenthesis.
Is this the correct graph of y=−13x+4
?(1 point)
Responses

Yes, it is the correct graph because this graph has a y
-intercept of (0,4)
.
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 4 right parenthesis .

Yes, it is the correct graph because this graph has a y
-intercept of (0,3)
.
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 3 right parenthesis .

No, it is not the correct graph because this graph has a positive slope.
No, it is not the correct graph because this graph has a positive slope.

No, it is not the correct graph because this graph used (0,3)
as the y
-intercept.

Answer 1

To determine if the graph correctly represents the equation $y=-\frac{1}{3}x+4$, we need to analyze its y-intercept and slope.

1. Y-intercept: The y-intercept of the equation $y=-\frac{1}{3}x+4$ is the point where $x=0$. Substituting $x=0$:

   $$y=-\frac{1}{3}(0)+4=4$$

   So, the y-intercept is $(0,4)$.

2. Slope: The slope of the equation $y=-\frac{1}{3}x+4$ is $-\frac{1}{3}$, which is negative, meaning the line should decrease as it moves from left to right.

Now, comparing this information to the plotted points provided:

• The graph shows points $(0,3)$ and $(3,2)$.

For the point $(0,3)$:

• At $x=0$, the graph shows $y=3$, not $y=4$. This is a discrepancy since the correct y-intercept should be $(0,4)$.

For the slope calculation:

• The slope from point $(0,3)$ to point $(3,2)$ is:

$$\text{slope}=\frac{2-3}{3-0}=\frac{-1}{3}$$

This slope is negative, which is consistent with the expected behavior of the line.

Final Assessment:

• The correct y-intercept for the line $y=-\frac{1}{3}x+4$ is $(0,4)$, but the graph shows the y-intercept as $(0,3)$, which is incorrect.

Correct Answer: No, it is not the correct graph because this graph used $(0,3)$ as the y-intercept.