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 (y2 – y1) ÷ (x2 – x1) = (3 – 1) ÷ (6 – 2) = 1/2 , 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.
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