SAT and ACT math terms · SAT Math, ACT Math
Slope
Also called: Rate of change
Slope: The rate of change of a line: how much y changes for each one-unit increase in x, calculated as rise over run.
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What it means
For two points (x₁, y₁) and (x₂, y₂), slope m = (y₂ − y₁) / (x₂ − x₁). A positive slope rises from left to right, a negative slope falls, a slope of zero is a horizontal line, and a vertical line has an undefined slope.
Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals, such as 2 and −1/2.
Example
The line through (1, 3) and (4, 9) has slope (9 − 3) / (4 − 1) = 6 / 3 = 2. In context, if x is hours and y is dollars, the slope means $2 per hour.
On the exam
Both tests ask you to interpret slope in context ('the slope represents…'), find it from a table or graph, and use parallel and perpendicular slopes.
Lessons and practice questions
Related terms
- Slope-intercept formThe form y = mx + b of a linear equation, where m is the slope and b is the y-intercept.
- Linear functionA function whose graph is a straight line, with a constant rate of change, written f(x) = mx + b.
- System of linear equationsTwo or more linear equations with the same variables, solved together to find values that satisfy all of them.