Finding Slope from Two Points
Free printable worksheets for finding the slope of a line from two points, with negative coordinates and fractions in lowest terms. Answer key included.
Each question gives two points and asks for the slope of the line through them: subtract the y-coordinates, subtract the x-coordinates in the same order, and divide. For (-2, 3) and (4, -1) that is -1 - 3 = -4 over 4 - (-2) = 6, so the slope is -4/6, or -2/3 in lowest terms.
Coordinates run from -9 to 9, so many questions mean subtracting a negative number. Half the slopes are positive and half negative, half are whole numbers and half fractions, and no line is horizontal or vertical. The answer key shows the change in y over the change in x first and then the slope in lowest terms, so a slip in the subtraction can be told from one in the simplifying.
What this worksheet covers
- Find the slope of a line through two points
- Subtract coordinates in the same order, including negative ones
Common Core standards
- 8.F.B.4 Determine the rate of change of a linear function from two (x, y) values or from a graph.
Frequently asked questions
What is the slope formula?
The change in y divided by the change in x: (y2 - y1) ÷ (x2 - x1), subtracting both coordinates in the same order. For (1, 2) and (5, 8) that is 6 ÷ 4, so the slope is 6/4, which is 3/2.
Does it matter which point comes first?
No, as long as both subtractions start from the same point. Going from (5, 8) back to (1, 2) gives -6 over -4, which is the same 3/2. Mixing the order, 8 - 2 over 1 - 5, gives the wrong sign.
Why does the answer key show two fractions?
The first, such as -4/6, is the change in y over the change in x before simplifying; the second, -2/3, is the slope in lowest terms. If the first is wrong, the subtraction went wrong; if only the second is, the simplifying did. When the first is already in lowest terms, it is printed once.
What grade is finding slope from two points?
Eighth grade, as part of finding the rate of change of a linear function. Students usually meet slope on a graph first, counting rise and run, and then find it from the coordinates alone.