Formula sheet · Grades 8 to 9

Algebra 1 formulas

7 formulas from this course. Each one gives the rule in math, one line on what it means, and a worked example that uses it.

Slope from two points

m = \frac{y_2 - y_1}{x_2 - x_1}

Slope is the change in y divided by the change in x.

y = b \Rightarrow m = 0,\qquad x = a \Rightarrow m \text{ undefined}

A horizontal line is flat, so its slope is zero; a vertical line does not run, so its slope is undefined.

y = mx + b

m is the slope and b is the y-intercept of the line.

x\text{-intercept: } y = 0,\qquad y\text{-intercept: } x = 0

Set one variable to zero and solve for the other to find where the line crosses an axis.

ax + b = c \Rightarrow x = \frac{c - b}{a}

Undo addition and subtraction first, then undo multiplication and division.

y = f(x) \Rightarrow \text{substitute } f(x) \text{ into the other equation}

Replace one variable with its equivalent expression, then solve one equation in one variable.

\text{opposite coefficients} \Rightarrow \text{add to cancel a variable}

Make one variable have opposite coefficients, then add the equations.

Practice problems with answers for every Algebra 1 topic.