The graph of y = f x - 11 is shown. The line slants sharply down from left to right.

Question

The graph of y = f x - 11 is shown. The line slants sharply down from left to right. The line passes through the following points: (negative 1 comma negative 2) (0 comma negative 4) Which equation defines the linear function f ?

Accepted Answer

Choice B is correct. The graph of a line in the xy -plane can be represented by the equation y = m x + b , where m is the slope of the line and 0 , b is the y -intercept. The slope of a line that passes through the points x 1 , y 1 and x 2 , y 2 can be calculated using the formula m = y 2 - y 1 x 2 - x 1 . The line shown passes through the points - 1 , - 2 and 0 , - 4 . Substituting - 1 , - 2 and 0 , 4 for x 1 , y 1 and x 2 , y 2 , respectively, in the formula m = y 2 - y 1 x 2 - x 1 yields m = - 4 - - 2 0 - - 1 , which is equivalent to m = - 2 1 , or m = - 2 . Since the line shown passes through the point 0 , - 4 , it follows that b = - 4 . Substituting - 2 for m and - 4 for b in the equation y = m x + b yields y = - 2 x - 4 . It&rsquo;s given that the graph shown is the graph of y = f x - 11 . Substituting - 2 x - 4 for y in the equation y = f x - 11 yields - 2 x - 4 = f x - 11 . Adding 11 to both sides of this equation yields - 2 x + 7 = f x . Therefore, the equation f x = - 2 x + 7 defines the linear function f . Choice A 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-gr