AlgebraMediumSlope of a line through the origin and a point on another line
Algebra practice question
In the xy-plane, the line 3x + 2y = 12 and the line y = kx intersect at a point whose x-coordinate is 2, where k is a constant. What is the value of k?
Answer: 3/2 or 1.5
At x = 2 on the first line: 6 + 2y = 12, so y = 3. The point (2, 3) is on y = kx: 3 = 2k, so k = 3/2.
Common wrong answers
- If you answered 3
- 3 is the y-coordinate of the intersection, not k.
- If you answered 2/3
- 2/3 is x over y, the reciprocal.
- If you answered -3/2
- −3/2 is the slope of the first line, not of y = kx.
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