PSAT Math Multiple-Choice Question 678: Answer and Explanation

Question: 678

If x and y are variables and if c is a nonzero constant, which of the following choices would not necessarily have a y-intercept when graphed?

I. x = c

II. y = -c

III. y = cx

• A. I only
• B. I and II only
• C. II and III only
• D. None of the above

Correct Answer: A

Explanation:

(A) Look at each option to see whether it is an answer.

Option I: x = c is a vertical line at c. The line will cross the y-axis only if c = 0. Since we are told that c is a nonzero constant, this equation does not have a y-intercept.

Option II: y = -c is a horizontal line at the -c value. The line will cross the y-axis at -c. This option, therefore, must have a y-intercept.

Option III: y = cx is a line with slope c. Note that when x = 0, y = c(0) = 0. So the line has a y-intercept at 0.

Thus, only option I is true, which is choice (A).