The line slants gradually down from left to right.

The line passes through the following points:

(negative 8 comma 4)

(0 comma 2)

(8 comma 0)

Question

The graph of $y = f (x) + 14$ is shown. Which equation defines function $f$ ?

Accepted Answer

Choice A is correct. An equation for the graph shown can be written in slope-intercept form y = m x + b , where m is the slope of the graph and its y -intercept is 0 , b . Since the y -intercept of the graph shown is 0 , 2 , the value of b is 2 . Since the graph also passes through the point 4 , 1 , the slope can be calculated as 1 - 2 4 - 0 , or - 1 4 . Therefore, the value of m is - 1 4 . Substituting - 1 4 for m and 2 for b in the equation y = m x + b yields y = - 1 4 x + 2 . It&rsquo;s given that an equation for the graph shown is y = f x + 14 . Substituting f x + 14 for y in the equation y = - 1 4 x + 2 yields f x + 14 = - 1 4 x + 2 . Subtracting 14 from both sides of this equation yields f x = - 1 4 x - 12 . Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Question the-li