How to use the slope and line equation worksheet generator
- Enter the number of problems, from 1 to 30, and a worksheet number. The same number always makes the same sheet.
- Choose whether slopes are whole numbers or may be fractions.
- Choose to ask for the slope and equation, or the slope only.
- Tick Show the answer key to see each answer, then print the sheet.
Formula
Slope m = (y2 - y1) / (x2 - x1), reduced to lowest terms
Y-intercept b = y1 - m x1
Equation: y = m x + b
Check by putting either point in the equation. Both must satisfy it.
Every problem is built from a slope and an intercept that work out to whole numbers or simple fractions, so the answers are clean.
The first problems of worksheet number 1
Problem 1: a line passes through (0, -9) and (3, -3). The slope is (-3 - -9) / (3 - 0) = 2, the y-intercept is -9, and the equation is y = 2x - 9. Problem 2 passes through (0, -4) and (3, 14), so m = 6, b = -4 and y = 6x - 4.
Problem 3 passes through (-1, 10) and (1, 8): m = -1, b = 9 and y = -x + 9. With fractions on, a line through (0, -4) and (9, -10) has m = -2/3, b = -4 and y = (-2/3)x - 4, and one through (6, -1) and (9, 0) has m = 1/3 and b = -3.
Using the sheets
Begin with whole-number slopes and the slope only, so students focus on rise over run and on the sign. Then add the intercept and equation. Fractions bring in reducing and make the sign of the intercept harder to track. Ask students to check each answer by substituting a point, a habit that catches most sign errors.
For a quick check of a slope, use the slope calculator. For more kinds of arithmetic practice, see the math worksheet generator.
Common mistakes
Students often subtract in different orders for the top and bottom, which flips the sign. Others forget that a negative divided by a negative is positive, or they read the intercept from the wrong point. Remind students to subtract in the same order in both, and to find the intercept by solving, not by guessing.
The next topic is often quadratics, which you can check with the quadratic equation solver. To work with fractions, see the fraction calculator.
Assumptions and limits
- Points have whole-number coordinates, and the line is not vertical.
- Slopes and intercepts are whole numbers or fractions in lowest terms, with whole-number intercepts.
- The same worksheet number, options and count always make the same sheet.
- The sheet is general practice and is not matched to a particular curriculum.
Frequently asked questions
How do you find the equation of a line through two points?
Find the slope as rise over run, then solve for the y-intercept using one point, and write y = m x + b.
How do I make a different sheet?
Change the worksheet number. The same number always makes the same problems.
Can I print an answer key?
Yes. Tick Show the answer key and print again with the same number.
What if I want only slopes?
Choose Slope only. Each problem then asks for the slope of the line through two points.