Math · Coordinate Geometry
Equation of a Line in Slope-Intercept Form
Medium
Math
Coordinate Geometry
Question
A line has slope 3 and y-intercept 1. Write its equation in slope-intercept form.
Answer choices
- y = 3x - 1
- y = -3x + 1
- y = 4x + 1
- y = 3x
- y = 3x + 1
E Correct answer: E) y = 3x + 1
Set up the problem carefully before computing. y = mx + b is the standard slope-intercept form. m is the slope, b is the y-intercept.
Carry the arithmetic through one step at a time, double-checking signs and units. The ACT writes wrong answers to catch the most common slips, so an answer that "looks right" without verification is risky.
Plug the answer back into the original expression as a sanity check whenever the problem allows. If the substitution does not balance, you have made an arithmetic mistake earlier in the work.
The underlying rule
Slope-intercept form is y = mx + b. With m = 3 and b = 1, the line is y = 3x + 1.
Why each wrong answer is wrong
- A) y = 3x - 1: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- B) y = -3x + 1: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- C) y = 4x + 1: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) y = 3x: A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
Slope-intercept form: y = mx + b. m is slope (rise/run); b is the y-intercept (where the line crosses the y-axis).
More Medium Coordinate Geometry
- Slope Between Two PointsWhat is the slope of the line passing through (2, 4) and (5, 6)?
- Distance Between Two PointsWhat is the distance between (1, 2) and (5, 6)?
- Midpoint of a SegmentWhat is the midpoint of the segment with endpoints (6, 6) and (-2, -2)?
- Slope Between Two PointsWhat is the slope of the line passing through (1, -1) and (5, 1)?
- Distance Between Two PointsWhat is the distance between (2, 0) and (6, 4)?