Question
Is this the correct graph of y=−1/3x+4 ?(1 point) 0,3 and 3,2..
Answers
Answer
Is this the correct graph of y=−1/3x+4 ?(1 point) Responses 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 used (0,3) as the y -intercept. No, it is not the correct graph because this graph used left parenthesis 0 comma 3 right parenthesis as the y -intercept. 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 . 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.
Answered by
GPT-4o mini
To determine if the points (0, 3) and (3, 2) lie on the graph of the equation \( y = -\frac{1}{3}x + 4 \), we can substitute the x-values of the points into the equation to see if the corresponding y-values match.
1. For the point (0, 3):
\[
y = -\frac{1}{3}(0) + 4 = 4
\]
The y-value is 4, not 3. So (0, 3) is **not** on the graph.
2. For the point (3, 2):
\[
y = -\frac{1}{3}(3) + 4 = -1 + 4 = 3
\]
The y-value is 3, not 2. So (3, 2) is **not** on the graph.
Neither of the given points lies on the graph of the equation \( y = -\frac{1}{3}x + 4 \).
1. For the point (0, 3):
\[
y = -\frac{1}{3}(0) + 4 = 4
\]
The y-value is 4, not 3. So (0, 3) is **not** on the graph.
2. For the point (3, 2):
\[
y = -\frac{1}{3}(3) + 4 = -1 + 4 = 3
\]
The y-value is 3, not 2. So (3, 2) is **not** on the graph.
Neither of the given points lies on the graph of the equation \( y = -\frac{1}{3}x + 4 \).
Answered by
GPT-4o mini
The correct graph of the equation \( y = -\frac{1}{3}x + 4 \) has the following key features:
1. **Y-intercept**: The y-intercept occurs where \( x = 0 \):
\[
y = -\frac{1}{3}(0) + 4 = 4.
\]
Thus, the y-intercept is \( (0, 4) \).
2. **Slope**: The slope of the line is \( -\frac{1}{3} \), indicating that it is a decreasing line (as x increases, y decreases).
Given the options:
- **Yes, it is the correct graph because this graph has a y-intercept of (0, 4)** is correct.
- Any options stating that the y-intercept is \( (0, 3) \) are incorrect.
- The options claiming that it has a positive slope are also incorrect, as the slope is negative.
So the correct response is:
**Yes, it is the correct graph because this graph has a y-intercept of (0, 4).**
1. **Y-intercept**: The y-intercept occurs where \( x = 0 \):
\[
y = -\frac{1}{3}(0) + 4 = 4.
\]
Thus, the y-intercept is \( (0, 4) \).
2. **Slope**: The slope of the line is \( -\frac{1}{3} \), indicating that it is a decreasing line (as x increases, y decreases).
Given the options:
- **Yes, it is the correct graph because this graph has a y-intercept of (0, 4)** is correct.
- Any options stating that the y-intercept is \( (0, 3) \) are incorrect.
- The options claiming that it has a positive slope are also incorrect, as the slope is negative.
So the correct response is:
**Yes, it is the correct graph because this graph has a y-intercept of (0, 4).**