Math · Coordinate Geometry
Slope Between Two Points
Medium
Math
Coordinate Geometry
Question
What is the slope of the line passing through (2, 4) and (5, 6)?
Answer choices
- 0
- 1.5
- 0.66666666666667
- undefined
- -0.66666666666667
C Correct answer: C) 0.66666666666667
Set up the problem carefully before computing. Slope is rise over run. Subtract y-values for the rise; subtract x-values (in the same order) for the run.
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 = (y2 - y1)/(x2 - x1) = (6 - 4)/(5 - 2) = 2/3 = 0.66666666666667.
Why each wrong answer is wrong
- A) 0: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- B) 1.5: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) undefined: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- E) -0.66666666666667: A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
Slope = (y2 - y1)/(x2 - x1). Always subtract the y-values and x-values in the same order, or you will get the wrong sign.
More Medium Coordinate Geometry
- 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)?
- Equation of a Line in Slope-Intercept FormA line has slope 3 and y-intercept 1. Write its equation in slope-intercept form.
- 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)?