Algebra Practice: Equations, Slope, Systems and Quadratics
Algebra 1 is usually grade 8 or 9. Strong 7th graders can stretch into it with support.
Algebra is the language of patterns. Once you can write a relationship as an equation, you can solve it, graph it and predict with it.
Linear equations and slope
A line can be written y = mx + b. The slope m is how much y changes for each 1 step in x, and b is where the line crosses the y-axis.
Systems of equations
Two equations with two unknowns can be solved by substitution or by adding the equations to cancel a variable.
Quadratics
Equations with x^2 can often be solved by factoring into two parentheses and setting each one to zero.
Worked examples
Slope through (2, 1) and (6, 9)
- Rise: 9 - 1 = 8
- Run: 6 - 2 = 4
- Slope = 8 / 4 = 2
Solve y = 2x and x + y = 12
- Substitute: x + 2x = 12
- 3x = 12, so x = 4
- y = 2 x 4 = 8
Solve x^2 + x - 12 = 0
- Numbers that multiply to -12 and add to 1: 4 and -3
- (x + 4)(x - 3) = 0
- x = -4 or x = 3
Practice challenge
4 problems with step-by-step answers. Nothing is saved.
Problem 1 of 4 · Linear equations
Solve 5(x - 2) = 15
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