16Hit1600
AlgebraHardx-intercept from a slope and a point

Algebra practice question

A line in the xy-plane has slope −2/3 and passes through the point (6, 1). At what value of x does the line cross the x-axis?

Answer: 15/2 or 7.5

From (6, 1) with slope −2/3: y − 1 = −(2/3)(x − 6). Set y = 0: −1 = −(2/3)(x − 6) → x − 6 = 3/2 → x = 15/2 = 7.5. (The y-intercept is 5, and 5 ÷ (2/3) = 7.5.)

Common wrong answers

If you answered 5
5 is the y-intercept, not the x-intercept.
If you answered 9
9 comes from using slope −1/3 (moving 3 right for each 1 down).
If you answered 4.5
4.5 comes from x − 6 = −3/2, a sign slip.

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