AlgebraVery hardValue on a line through two points
Algebra practice question
A line in the xy-plane passes through the points (2, 7) and (6, 19). What is the y-coordinate of the point on the line whose x-coordinate is 10?
Answer: 31
Slope: (19 − 7)/(6 − 2) = 12/4 = 3. From (6, 19), moving 4 more units in x raises y by 12: 19 + 12 = 31. (The line is y = 3x + 1, and 3(10) + 1 = 31.)
Common wrong answers
- If you answered 13
- 13 is 7 + 6, adding the y-value of one point to the x-value of the other. Use the slope.
- If you answered 30
- 30 is 3 × 10, the slope times x, without the intercept. The line is y = 3x + 1.
- If you answered 37
- 37 would come from adding the full 18-unit change again; from x = 6 to x = 10 is only 4 units, so y rises by 12.
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