AlgebraHardx-intercept from a slope and a point
Algebra practice question
A line with slope −4/3 passes through the point (6, 1). The line crosses the x-axis at (a, 0). What is the value of a? (Enter your answer as a fraction or decimal.)
Answer: 27/4 or 6.75
Falling from y = 1 at slope −4/3 reaches y = 0 after a run of 1 ÷ (4/3) = 3/4. So a = 6 + 3/4 = 27/4.
Common wrong answers
- If you answered 6
- 6 is the x-coordinate of the given point, not of the intercept.
- If you answered 21/4
- You moved left from x = 6; with a negative slope and positive y, the line descends to the right: a = 6 + 3/4.
- If you answered 7.33
- The run to the axis is 3/4, not 4/3: dividing rise 1 by slope magnitude 4/3 gives 3/4.
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