AlgebraMediumFinding an x-intercept
Algebra practice question
A line in the xy-plane is represented by the equation 5x − 2y = 20.
The line crosses the x-axis at the point (a, 0). What is the value of a?
Answer: 4
Every point on the x-axis has y = 0. Substitute: 5x − 2(0) = 20, so 5x = 20 and x = 4. The x-intercept is (4, 0).
Common wrong answers
- If you answered 20
- 20 is 5x, one step short. Divide by 5 to get x = 4.
- If you answered −10
- −10 is the y-intercept, from setting x = 0: −2y = 20. The x-intercept is where y = 0 instead.
- If you answered −4
- The sign is wrong: 5x = 20 gives x = +4. Setting y = 0 removes the −2y term entirely, so no negative is introduced.
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