➕ Algebra 1 · Linear Functions
Slope of a Line: true or false
Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.
All statements and answers
A line that goes up from left to right has a positive slope.
✓ True. Rising as you move right means a positive rise and run, so a positive slope.
A horizontal line has an undefined slope.
✗ False. A horizontal line has slope 0. A vertical line is the one with undefined slope.
The slope of a vertical line is 0.
✗ False. A vertical line has no run, and dividing by 0 is undefined.
The slope through (2, 3) and (6, 11) is 2.
✓ True. (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2.
Slope is run divided by rise.
✗ False. Slope is rise divided by run.
Computing (y2 − y1) ÷ (x1 − x2) always gives the right slope.
✗ False. Mixing the order flips the sign (except when the slope is 0). Use the same order on top and bottom.
A line with slope −3 goes down 3 units for every 1 unit to the right.
✓ True. −3 = −3/1: down 3 (rise −3), right 1 (run 1).
A line with slope −5 is less steep than a line with slope 2, because −5 is smaller than 2.
✗ False. Steepness is the absolute value of the slope (its distance from 0). A line with slope −5 is steeper than a line with slope 2, even though −5 is the smaller number.
The slope between any two points on the same straight line is the same.
✓ True. A line has the same steepness everywhere, so every rise-over-run ratio matches.
A rate such as “10 dollars per hour” is a slope.
✓ True. “Per” signals a rate of change: how much y changes for each 1 unit of x.