Digital PSAT Math Practice Question 268: Answer and Explanation

Question: 268

For how many points in the xy-coordinate plane will the functions y = 4x and 2y = 8x - 5 intersect?

• A. Infinitely many
• B. 2
• C. 1
• D. None

Correct Answer: D

Explanation:

(D) Get the second equation into slope-intercept form so you can see how the two equations relate. In order to accomplish this, divide both sides by 2:

y = 4x - 2.5

Therefore, both lines have the same slope, but different y-intercepts. This means that they're parallel lines and never intersect, choice (D).

Alternatively, if you don't recognize this right away, you can set the right side of both equations (in slope-intercept form) equal to each other and attempt to solve for x to see where the two lines intersect:

4x = 4x - 2.5

Subtracting 4x from both sides, you have 0 = - 2.5, which is a false statement, so there are no solutions to this equation, and hence no intersection points.