PSAT Math Multiple-Choice Question 628: Answer and Explanation

Question: 628

Line A has points (1, -2) and (-1, 0). Line B has point (3, 4). What would the y-value of the y-intercept of line B need to be in order for line A and line B to intersect at a 90° angle?

• A. -7
• B. -1
• C. 1
• D. 4

Correct Answer: C

Explanation:

(C) Let's first find the slope of line A. The formula for slope is Change in y/Change in x:

If the lines are to intersect at a 90° angle, they must be perpendicular. Any line perpendicular to this one would have a slope of 1, since 1 is the negative reciprocal of -1.

We can now use the one given point of line B and the slope in the point-slope formula in order to get the equation of line B.

The point-slope formula is given by the equation y - y₁ = m(x - x₁):

y - 4 = 1(x - 3)

Distributing the 1 gives:

y - 4 = x - 3

To get the line into slope-intercept form, add 4 to both sides:

y = x + 1

Therefore, line B has a y-intercept of 1, which is answer (C).

Alternatively, once it is known that the slope of the new line is 1, the equation must be y = x + b. Plug in the point (3, 4) to the line to solve for b:

4 = 3 + b → b = 1