PSAT Math Multiple-Choice Question 56: Answer and Explanation

Question: 56

The table above shows selected values for the linear function f(x). What is the value of j?

• A.
• B.
• C.
• D.

Correct Answer: B

Explanation:

B

The question asks for the value of a variable in the table. Since the values in the table are part of a linear function, they must all lie on the same line. Recall that, in function notation, the number inside the parentheses is the x-value that goes into the function, and the value that comes out of the function is the y-value. Plug the x- and y-values into the slope formula to find the value of j. The slope formula is . Plug the two known points, (-1, 2) and (5, -6), into the equation. The equation becomes . Now use the slope of the line and one of the known points to solve for j. Plug (j, j) and (-1, 2) into the slope equation. The equation becomes . Cross-multiply to get -4(-1 - j) = 3(2 - j), or 4 + 4j = 6 - 3j. Add 3j to both sides and subtract 4 from both sides to get 7j = 2. Divide both sides by 7 to get j = . The correct answer is (B).