Compare the function 3x + 2y = 12 to the function graphed in the following image.
A line is graphed on a coordinate plane. The line passes through the points just above left-parenthesis negative 2 comma 6 right-parenthesis and left-parenthesis 6 comma negative 2 right-parenthesis.
Which of the following is a true statement?
(1 point)
Responses
The y-intercept of the graphed function is greater than the y-intercept of the function 3x + 2y = 12.
The y -intercept of the graphed function is greater than the y -intercept of the function 3 x + 2 y = 12.
The x-intercept of the graphed function is greater than the x-intercept of the function 3x + 2y = 12.
The x -intercept of the graphed function is greater than the x -intercept of the function 3 x + 2 y = 12.
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 graphed function does not pass through the y-axis (0, y). Therefore, the y-intercept of the graphed function is not greater than the y-intercept of the function 3x + 2y = 12.
The graphed function does pass through the x-axis (x, 0) at x = 4. Therefore, the x-intercept of the graphed function (4) is greater than the x-intercept of the function 3x + 2y = 12 (x-intercept is 4/3).
Since the graphed function does not pass through the y-axis (0, y), the y-intercept of the graphed function is not the same as the y-intercept of the function 3x + 2y = 12.
Therefore, the correct statement is: The x-intercept of the graphed function is greater than the x-intercept of the function 3x + 2y = 12.