Grade 8 · Algebra · Linear Patterns and Equations

Connect Linear Representations

A linear relationship can be described by y = mx + b, where m is the constant rate and b is the initial value when x = 0.

The big idea

Rate and initial value tell different parts of the story

Two plans can grow at the same rate but start at different values, or start together and change at different rates. Both features determine when their values meet.

Work it through

Solve 3x + 5 = 2x + 17

1. Subtract 2x from both sides: x + 5 = 17.
2. Subtract 5 from both sides: x = 12.
3. Check the left side: 3(12) + 5 = 41.
4. Check the right side: 2(12) + 17 = 41.

For parents and educators

Ontario curriculum alignment

Grade 8 Mathematics · Strand C: Algebra

View supported expectations

C1.1 · Patterns

Identify and compare repeating, growing, and shrinking patterns, and compare linear growing and shrinking patterns on the basis of their constant rates and initial values.
C1.2 · Patterns

Create and translate repeating, growing, and shrinking patterns involving rational numbers using representations including algebraic expressions and equations.
C2.1 · Variables and Expressions

Add and subtract monomials with a degree of 1, and add binomials with a degree of 1 that involve integers, using tools.
C2.2 · Variables and Expressions

Evaluate algebraic expressions that involve rational numbers.
C2.3 · Equalities and Inequalities

Solve equations that involve multiple terms, integers, and decimal numbers in various contexts, and verify solutions.
C2.4 · Equalities and Inequalities

Solve inequalities that involve integers, and verify and graph the solutions.