Linear Functions • Topic 1 of 7

Slope

Slope measures the steepness and direction of a line: rise over run, the change in y for each unit change in x. A positive slope rises left to right, a negative slope falls, a zero slope is horizontal, and a vertical line has undefined slope. In y = mx + b, the slope is m. Parallel lines share the same slope; perpendicular lines have slopes whose product is −1 (negative reciprocals). Reading slope from a graph, an equation or a table is one of the most frequently tested SAT skills.

✅ Solved examples

1. What is the slope of y = 3x + 2?
In y = mx + b the slope is the coefficient of x, so m = 3.
2. A line rises 6 units over a run of 2. What is its slope?
Slope = rise/run = 6/2 = 3.
3. What is the slope of a horizontal line?
No vertical change, so slope = 0.
4. What is the slope of y = −x + 5?
The coefficient of x is −1, so the slope is −1.

✏️ Practice — try these, take hints as needed

1. What is the slope of y = 4x − 7?
Identify the coefficient of x.
It is m in y = mx + b.
—
4.
2. A line rises 10 over a run of 5. Slope?
Slope = rise/run.
10 ÷ 5.
—
2.
3. What is the slope of a vertical line?
Run is zero.
Division by zero.
—
Undefined.
4. What is the slope of y = −2x + 1?
Coefficient of x.
Include the sign.
−2.
−2.
5. A line through (0,0) and (4,8). What is its slope?
Slope = (8 − 0)/(4 − 0).
8/4.
—
2.

📝 Topic test — 8 questions

Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.

Loading questions…
Rate of Change →