Question
Is this the correct graph of y = -1/3x + 4?
The graph has two dotted points (0,3) and (3,2)
A. Yes it is the correct graph because this graph has a y-intercept of (0, 4)
B. No it’s not the correct graph because this graph used (0, 3) as the y-intercept
C. Yes it is the correct graph because this graph has a y-intercept of (0,3)
D. No it is not the correct graph because this graph has a positive slope
The graph has two dotted points (0,3) and (3,2)
A. Yes it is the correct graph because this graph has a y-intercept of (0, 4)
B. No it’s not the correct graph because this graph used (0, 3) as the y-intercept
C. Yes it is the correct graph because this graph has a y-intercept of (0,3)
D. No it is not the correct graph because this graph has a positive slope
Answers
Answered by
GPT-4o mini
To determine if the provided graph is correct for the equation \( y = -\frac{1}{3}x + 4 \), we can analyze the components of the equation.
1. **Y-intercept**: The y-intercept of the line is where \( x = 0 \). Plugging \( x = 0 \) into the equation gives:
\[
y = -\frac{1}{3}(0) + 4 = 4.
\]
Therefore, the y-intercept is \( (0, 4) \).
2. **Slope**: The slope of the line is \( -\frac{1}{3} \), which is negative. This means the line should be decreasing as you move from left to right.
3. **Dotted Points**:
- \( (0, 3) \): This is not the y-intercept, so it's not on the line.
- \( (3, 2) \): To find if this point is on the line, substitute \( x = 3 \):
\[
y = -\frac{1}{3}(3) + 4 = -1 + 4 = 3.
\]
The correct y-value when \( x = 3 \) is 3, not 2. Thus, \( (3, 2) \) is also not on the line.
Given this analysis, we can conclude:
- The graph does not show the correct y-intercept, and the points do not satisfy the equation.
Now let's evaluate the answer choices:
A. Yes, it is the correct graph because this graph has a y-intercept of (0, 4) - **Incorrect** (this statement is correct but the graph does not match).
B. No, it’s not the correct graph because this graph used (0, 3) as the y-intercept - **Correct** (the graph wrongly has (0, 3) as the y-intercept).
C. Yes, it is the correct graph because this graph has a y-intercept of (0, 3) - **Incorrect** (the y-intercept is (0, 4)).
D. No, it is not the correct graph because this graph has a positive slope - **Incorrect** (the slope is negative, not positive).
The correct answer is **B**: No, it’s not the correct graph because this graph used (0, 3) as the y-intercept.
1. **Y-intercept**: The y-intercept of the line is where \( x = 0 \). Plugging \( x = 0 \) into the equation gives:
\[
y = -\frac{1}{3}(0) + 4 = 4.
\]
Therefore, the y-intercept is \( (0, 4) \).
2. **Slope**: The slope of the line is \( -\frac{1}{3} \), which is negative. This means the line should be decreasing as you move from left to right.
3. **Dotted Points**:
- \( (0, 3) \): This is not the y-intercept, so it's not on the line.
- \( (3, 2) \): To find if this point is on the line, substitute \( x = 3 \):
\[
y = -\frac{1}{3}(3) + 4 = -1 + 4 = 3.
\]
The correct y-value when \( x = 3 \) is 3, not 2. Thus, \( (3, 2) \) is also not on the line.
Given this analysis, we can conclude:
- The graph does not show the correct y-intercept, and the points do not satisfy the equation.
Now let's evaluate the answer choices:
A. Yes, it is the correct graph because this graph has a y-intercept of (0, 4) - **Incorrect** (this statement is correct but the graph does not match).
B. No, it’s not the correct graph because this graph used (0, 3) as the y-intercept - **Correct** (the graph wrongly has (0, 3) as the y-intercept).
C. Yes, it is the correct graph because this graph has a y-intercept of (0, 3) - **Incorrect** (the y-intercept is (0, 4)).
D. No, it is not the correct graph because this graph has a positive slope - **Incorrect** (the slope is negative, not positive).
The correct answer is **B**: No, it’s not the correct graph because this graph used (0, 3) as the y-intercept.
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