The line slants sharply down from left to right. The line passes through the following points: (negative 1 comma 7)

Question

The graph of the linear function $y = f (x) + 19$ is shown. If $c$ and $d$ are positive constants, which equation could define $f$ ?

Accepted Answer

Choice A is correct. It&rsquo;s given that the graph of the linear function y = f x + 19 is shown. This means that the graph of y = f x + 19 can be translated down 19 units to create the graph of y = f x and the y -coordinate of every point on the graph of y = f x + 19 can be decreased by 19 to find the resulting point on the graph of y = f x . The y -intercept of the graph of y = f x + 19 is 0 , 3 . Translating the graph of y = f x + 19 down 19 units results in a y -intercept of the graph of y = f x at the point 0 , 3 - 19 , or 0 , - 16 . The graph of y = f x + 19 slants down from left to right, so the slope of the graph is negative. The translation of a linear graph changes its position, but does not change its slope. It follows that the slope of the graph of y = f x is also negative. The equation of a linear function f can be written in the form f x = b + m x , where b is the y -coordinate of the y -intercept and m is the slope of the graph of y = f x . It's given that c and d are positive constants. Since the y -coordinate of the y -intercept and the slope of the graph of y = f x are both negative, it follows that f x = - d - c x could define f . Choice B is incorrect. This could define a linear function where its graph has a positive, not negative, y -intercept. Choice C is incorrect. This could define a linear function where its graph has a positive, not negative, slope. Choice D is incorrect. This could define a linear function where its graph has a positive, not negative, y -intercept and a positive, not negative, slope.

Question 2d19a5