The equation and the graph represent two linear functions.
Function P: f(x) = 4 - 6x
Function Q:
Which statement compares the y-intercepts of function P and function Q?
The y-intercept of function P is 4 which is greater than the y-intercept of function Q.
The y-intercept of a linear function is the value of the function when x equals zero. For function P, f(x) = 4 - 6x, substituting x = 0 gives us a y-intercept of 4. The y-intercept of function Q, which is not provided, is presumably less than 4 based on the options given.
This statement is incorrect because the y-intercept of function P is actually 4, not -6. Therefore, it cannot be less than the y-intercept of function Q.
This choice is inaccurate as it implies that the y-intercept of function Q is also 4. We do not have information to support that function Q has the same y-intercept, thus this statement cannot be concluded as true.
This option is also incorrect; it incorrectly states the y-intercept of function P as -6 instead of the correct value of 4. Therefore, it cannot be greater than the y-intercept of function Q.
This choice is correct, as it accurately identifies the y-intercept of function P as 4 and suggests it is greater than that of function Q, which aligns with the context of the question.
In summary, the y-intercept of function P is correctly identified as 4, which is greater than the unspecified y-intercept of function Q. This understanding is crucial when comparing linear functions, as the y-intercept provides insight into their graphical relationship. The other options present incorrect values or comparisons, reinforcing that option D is the only accurate statement regarding the y-intercepts of the functions in question.
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