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?
A
B
C
D
Correct answer: B
Explanation
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.
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id cb_question_bank:b7b794b9-cd71-4473-bf1f-0de552260713 · question 78391fcc · IBN 029517-DC
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