Question

Is this the correct graph of y= −1/3x + 4?
​
graph shows (0,3) (3,2)

A. No, it is not the correct graph because this graph used (0, 3) as the y-intercept.
B. Yes, it is the correct graph because this graph has a y-intercept of (0,3).
C. Yes, it is the correct graph because this graph has a y-intercept of (0,4).
D. No, it is not the correct graph because this graph has a positive slope.

Answer 1

To determine whether the graph represents the equation \( y = -\frac{1}{3}x + 4 \), we need to analyze the components of the equation.

1. **Y-Intercept**: The y-intercept occurs when \( x = 0 \). Plugging \( x = 0 \) into the equation:
\[
y = -\frac{1}{3}(0) + 4 = 4
\]
So, the y-intercept of the line is \( (0, 4) \).

2. **Slope**: The slope of the line is \( -\frac{1}{3} \), which indicates that the line decreases as \( x \) increases (i.e., it has a negative slope).

Given that the proposed graph shows the point \( (0, 3) \), which does not match the y-intercept of \( (0, 4) \), the graph is incorrect.

Now, looking at the options provided:

A. No, it is not the correct graph because this graph used (0, 3) as the y-intercept.
B. Yes, it is the correct graph because this graph has a y-intercept of (0, 3).
C. Yes, it is the correct graph because this graph has a y-intercept of (0, 4).
D. No, it is not the correct graph because this graph has a positive slope.

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