AlgebraVery hardSharing an x-intercept with a given line
Algebra practice question
In the xy-plane, line ℓ has the equation 5x − 2y = 20. Line m has the same x-intercept as ℓ and a y-intercept of 5. If line m is written as y = ax + b, what is the value of a + b?
Answer: 3.75 or 15/4
ℓ meets the x-axis at (4, 0). Line m passes through (4, 0) and (0, 5), so its slope is −5/4 and a + b = −5/4 + 5 = 15/4.
Common wrong answers
- If you answered 6.25
- 6.25 uses slope +5/4.
- If you answered 7.5
- 7.5 uses slope 5/2, the slope of ℓ.
- If you answered -5
- −5 uses the y-intercept of ℓ.
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