AlgebraVery hardSlope that is also a coordinate
Algebra practice question
In the xy-plane, the line y = kx + 3, where k is a positive constant, passes through the point (k, 7). What is the value of k?
Answer: 2
Substitute x = k, y = 7: 7 = k · k + 3, so k² = 4 and k = 2 (positive). Check: y = 2x + 3 passes through (2, 7).
Common wrong answers
- If you answered 4
- 4 is k², one step short.
- If you answered 7
- 7 is the y-coordinate of the point, not k.
- If you answered -2
- −2 also squares to 4, but k must be positive.
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