16Hit1600
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?

  1. A. y = 2x − 5Correct
  2. B. y = 2x + 1
  3. C. y = 2x + 7
  4. 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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