Compare the function 3x + 2y = 8
to the function graphed below and then identify which statement is true.
Responses
The y-intercept of the graphed function is greater than the y-intercept of the function 3x + 2y = 8.
The y-intercept of the graphed function is greater than the y-intercept of the function 3x + 2y = 8.
The two functions have the same x-intercept.
The two functions have the same x-intercept.
The two functions have the same y-intercept.
The two functions have the same y-intercept.
The x-intercept of 3x + 2y = 8 is greater than the x-intercept of the graphed function.
Unfortunately, I am unable to view the graphed function since my capabilities do not include the ability to see or interpret images. However, I can discuss the x-intercept and the y-intercept of the given function \(3x + 2y = 8\) to assist you in making a comparison if you provide information regarding the graphed function.
For the function \(3x + 2y = 8\):
The y-intercept occurs where \(x = 0\). By setting \(x = 0\), we get \(2y = 8\), so \(y = \frac{8}{2} = 4\). Therefore, the y-intercept of \(3x + 2y = 8\) is at the point \((0, 4)\) on the y-axis.
The x-intercept occurs where \(y = 0\). By setting \(y = 0\), we get \(3x = 8\), so \(x = \frac{8}{3}\). Therefore, the x-intercept of \(3x + 2y = 8\) is at the point \((\frac{8}{3}, 0)\) on the x-axis.
Without seeing the graphed function:
- If the y-intercept of the graphed function is any value greater than 4, then the statement "The y-intercept of the graphed function is greater than the y-intercept of the function \(3x + 2y = 8\)" is true.
- If the graphed function has the same point (0, 4) as its y-intercept, the statement "The two functions have the same y-intercept" is true.
- If the graphed function crosses the x-axis at \((\frac{8}{3}, 0)\), then the statement "The two functions have the same x-intercept" is true.
- If the x-intercept of the graphed function is any x-value less than \(\frac{8}{3}\), then the statement "The x-intercept of \(3x + 2y = 8\) is greater than the x-intercept of the graphed function" is true.
Please provide details about the graphed function, and I can offer more specific information.