AlgebraHardSum of a line's intercepts
Algebra practice question
In the xy-plane, a line passes through (−2, 7) and (4, 1). What is the sum of the line's x-intercept and y-intercept?
Answer: 10
Slope (1 − 7)/(4 + 2) = −1, so y = −x + b; 7 = 2 + b gives b = 5. The y-intercept is 5 and, setting y = 0, the x-intercept is also 5. Sum: 10.
Common wrong answers
- If you answered 0
- 0 comes from taking the x-intercept as −5.
- If you answered 5
- 5 is one intercept alone.
- If you answered -1
- −1 is the slope.
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