x f ( x ) 21 18 15 12 The table above shows some values of x and their corresponding

Question

x f ( x ) 21 18 15 12 The table above shows some values of x and their corresponding values for the linear function f . What is the x -intercept of the graph of in the xy -plane?

Accepted Answer

Choice B is correct. The equation of a linear function can be written in the form , where , m is the slope of the graph of , and b is the y -coordinate of the y -intercept of the graph. The value of m can be found using the slope formula, . According to the table, the points and lie on the graph of . Using these two points in the slope formula yields , or . Substituting for m in the slope-intercept form of the equation yields . The value of b can be found by substituting values from the table and solving; for example, substituting the coordinates of the point into the equation gives , which yields . This means the function given by the table can be represented by the equation . The value of the x -intercept of the graph of can be determined by finding the value of x when . Substituting into yields , or . This corresponds to the point . Choice A is incorrect and may result from substituting the value of the slope for the x -coordinate of the x -intercept. Choice C is incorrect and may result from a calculation error. Choice D is incorrect and may result from substituting the y -coordinate of the y -intercept for the x -coordinate of the x -intercept.

x	$negative 11$	$negative 10$	$negative 9$	$negative 8$
f(x)	21	18	15	12

Question x-f-x-