Math Problem of the Week - Algebra and Up - Mar. 27, 2022 to Apr. 2, 2022

Algebra and Up: 

Question: There are two perpendicular lines graphed on a plane. Line A goes through the points (2,1) and (6, 3). Line B goes through (2, 1) and (x, 5). Solve for x. 

Answer: x = 0

Solution: 

To solve for x, we need to know the slope of Line B. Line A and Line B are perpendicular, so the slope of Line B is the opposite of the reciprocal of the slope of Line A. Line A’s slope is ½, so the slope of Line B must be –2. Now that we have a point on the line and its slope, we can write an equation in slope-intercept form:

y = –2x + b

y = 1   x = 2

1 = –4 + b

b = 5

y = –2x + 5

5 is the y–intercept. When y = 5, then x = 0.