Once you can read slope off a graph, the algebraic version is the same idea with no picture: subtract the y-values, subtract the x-values in the same order, and divide.
The skill is short but it has the highest error rate in the unit because of sign mistakes. Writing the formula out every time, with parentheses around negative numbers, prevents most of them.
How to solve it, step by step
Label the points
Call one point (x₁, y₁) and the other (x₂, y₂). It does not matter which is which, as long as you stay consistent.
Write the slope formula
m = (y₂ − y₁) / (x₂ − x₁). Write it every time; do not do it in your head.
Substitute with parentheses
Put parentheses around every negative coordinate: m = (1 − (−3)) / (2 − (−4)). Subtracting a negative becomes addition.
Simplify numerator and denominator separately
1 − (−3) = 4 and 2 − (−4) = 6, so m = 4/6.
Reduce the fraction
4/6 = 2/3. If the denominator is 0 the slope is undefined; if the numerator is 0 the slope is 0.
Worked example
Find the slope of the line through (−5, 7) and (3, −9).
- (x₁, y₁) = (−5, 7) (x₂, y₂) = (3, −9)
- m = (−9 − 7) / (3 − (−5))
- m = (−16) / (8)
- m = −2
Answer m = −2
Find the slope through (4, −2) and (4, 6).
- m = (6 − (−2)) / (4 − 4)
- m = 8 / 0
Answer Undefined (vertical line x = 4)
Mistakes DeltaMath marks wrong
- Mixing the order: (y₂ − y₁) over (x₁ − x₂) flips the sign of the answer.
- Dropping parentheses so that 3 − −5 gets computed as 3 − 5.
- Writing 8/0 as 0. Division by zero is undefined, not zero.
- Leaving a fraction like −16/8 unreduced when the answer is a whole number.
How to type the answer
- Integers: -2, 0, 5. Fractions: 3/4, -5/2.
- Type "undefined" (or pick it from the options) for vertical lines.
- Do not include "m =" in the answer box.