Question
Compare the function: 3x + 2y = 12, to the function graphed attached to identify the true statement.
A. The two functions have the same x-intercept.
B. The y-intercept of the graphed function is greater than the y-intercept of the function 3x + 2y = 12.
C. The two functions have the same y-intercept.
D. The x-intercept of the graphed function is greater than the x-intercept of the function 3x + 2y = 12.
A. The two functions have the same x-intercept.
B. The y-intercept of the graphed function is greater than the y-intercept of the function 3x + 2y = 12.
C. The two functions have the same y-intercept.
D. The x-intercept of the graphed function is greater than the x-intercept of the function 3x + 2y = 12.
Answers
GPT-4o mini
To accurately compare the function \(3x + 2y = 12\) with the function that is graphed, we need to determine the x-intercept and y-intercept of the given function.
1. **Finding the x-intercept of \(3x + 2y = 12\)**:
- Set \(y = 0\):
\[
3x + 2(0) = 12 \implies 3x = 12 \implies x = 4
\]
So, the x-intercept is \((4, 0)\).
2. **Finding the y-intercept of \(3x + 2y = 12\)**:
- Set \(x = 0\):
\[
3(0) + 2y = 12 \implies 2y = 12 \implies y = 6
\]
So, the y-intercept is \((0, 6)\).
With the intercepts calculated, we can evaluate the statements. However, to complete the comparison, we need information about the corresponding intercepts of the graph that has been mentioned but not shown.
Given that we have the x-intercept \( (4, 0) \) and y-intercept \( (0, 6) \):
- **Option A**: "The two functions have the same x-intercept." - This is true if the other function's x-intercept is also \(4\).
- **Option B**: "The y-intercept of the graphed function is greater than the y-intercept of the function \(3x + 2y = 12\)." - This is true if the other function's y-intercept is greater than \(6\).
- **Option C**: "The two functions have the same y-intercept." - This is true if the other function's y-intercept is also \(6\).
- **Option D**: "The x-intercept of the graphed function is greater than the x-intercept of the function \(3x + 2y = 12\)." - This is true if the other function's x-intercept is greater than \(4\).
Without the graph, we can't definitively pick an option, but you can apply the calculations above to the intercepts of the graphed function to see which statement is true.
1. **Finding the x-intercept of \(3x + 2y = 12\)**:
- Set \(y = 0\):
\[
3x + 2(0) = 12 \implies 3x = 12 \implies x = 4
\]
So, the x-intercept is \((4, 0)\).
2. **Finding the y-intercept of \(3x + 2y = 12\)**:
- Set \(x = 0\):
\[
3(0) + 2y = 12 \implies 2y = 12 \implies y = 6
\]
So, the y-intercept is \((0, 6)\).
With the intercepts calculated, we can evaluate the statements. However, to complete the comparison, we need information about the corresponding intercepts of the graph that has been mentioned but not shown.
Given that we have the x-intercept \( (4, 0) \) and y-intercept \( (0, 6) \):
- **Option A**: "The two functions have the same x-intercept." - This is true if the other function's x-intercept is also \(4\).
- **Option B**: "The y-intercept of the graphed function is greater than the y-intercept of the function \(3x + 2y = 12\)." - This is true if the other function's y-intercept is greater than \(6\).
- **Option C**: "The two functions have the same y-intercept." - This is true if the other function's y-intercept is also \(6\).
- **Option D**: "The x-intercept of the graphed function is greater than the x-intercept of the function \(3x + 2y = 12\)." - This is true if the other function's x-intercept is greater than \(4\).
Without the graph, we can't definitively pick an option, but you can apply the calculations above to the intercepts of the graphed function to see which statement is true.