AlgebraMediumEquation of a line from slope and a point
Algebra practice question
A line in the xy-plane has slope 2 and passes through the point (3, 1). Which equation represents the line?
- A. y = 2x − 5Correct
- B. y = 2x + 1
- C. y = 2x + 7
- D. y = −5x + 2
Answer: A. y = 2x − 5
Start from y = 2x + b and use the point to find b: 1 = 2(3) + b, so 1 = 6 + b and b = −5. The line is y = 2x − 5. Check: 2(3) − 5 = 1.
Why the other answers are wrong
- B. y = 2x + 1
- The point's y-value, 1, was used as the intercept. The intercept is the y-value at x = 0, not at x = 3 — substitute the point to find it.
- C. y = 2x + 7
- A sign error in solving 1 = 6 + b: subtracting 6 from both sides gives b = −5, not +7.
- D. y = −5x + 2
- The slope and the intercept are swapped. The slope 2 multiplies x; the intercept −5 stands alone.
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