Question
Graph showing (0,3) (3,2); Is this the correct graph of y= 1/3x + 4? (Yes, it is the correct graph because this graph has a y - intercept of (0, 3);
Answers
GPT-4o mini
To determine whether the graph of the line you've mentioned, \(y = \frac{1}{3}x + 4\), is correct based on the points (0, 3) and (3, 2), we should check the following:
1. **Y-Intercept Calculation**:
In the equation \(y = \frac{1}{3}x + 4\), the y-intercept (the value of \(y\) when \(x = 0\)) is given by:
\[
y = \frac{1}{3}(0) + 4 = 4
\]
So the y-intercept is \( (0, 4) \), not (0, 3).
2. **Checking the Point (3, 2)**:
Now let's see if the point (3, 2) lies on the line by substituting \(x = 3\):
\[
y = \frac{1}{3}(3) + 4 = 1 + 4 = 5
\]
Hence, the corresponding \(y\) value for \(x = 3\) is 5, not 2.
### Conclusion:
- The y-intercept of \(y = \frac{1}{3}x + 4\) is \( (0, 4) \), **not (0, 3)**.
- The point (3, 2) does **not lie on** the line.
Thus, the statement "Yes, it is the correct graph because this graph has a y-intercept of (0, 3)" is incorrect. The correct y-intercept is (0, 4), so the graph you have does not accurately represent the function \(y = \frac{1}{3}x + 4\).
1. **Y-Intercept Calculation**:
In the equation \(y = \frac{1}{3}x + 4\), the y-intercept (the value of \(y\) when \(x = 0\)) is given by:
\[
y = \frac{1}{3}(0) + 4 = 4
\]
So the y-intercept is \( (0, 4) \), not (0, 3).
2. **Checking the Point (3, 2)**:
Now let's see if the point (3, 2) lies on the line by substituting \(x = 3\):
\[
y = \frac{1}{3}(3) + 4 = 1 + 4 = 5
\]
Hence, the corresponding \(y\) value for \(x = 3\) is 5, not 2.
### Conclusion:
- The y-intercept of \(y = \frac{1}{3}x + 4\) is \( (0, 4) \), **not (0, 3)**.
- The point (3, 2) does **not lie on** the line.
Thus, the statement "Yes, it is the correct graph because this graph has a y-intercept of (0, 3)" is incorrect. The correct y-intercept is (0, 4), so the graph you have does not accurately represent the function \(y = \frac{1}{3}x + 4\).