Unit 5: Expressions and Equations (Slope Intercept)

Proportional vs. Non-Proportional Relationships:
Students will understand the connections between proportional relationships, lines, and linear equations.

Slope and Rate of Change:
They will know how to interpret the unit rate as the slope of a graph.

Graphing Fundamentals:
Students will know how to graph proportional relationships and identify key features like the origin, x-coordinates, y-coordinates, and ordered pairs.

Equation Forms:
They will understand how to derive and find equations in the forms y = mx and y = mx + b.

Graph and Analyze Proportional Relationships:
Interpret the unit rate as the slope of a graph and compare two different proportional relationships represented in different ways.

Derive and Solve Equations: Derive the equations y = mx and y = mx + b for lines passing through the origin or intercepting the vertical axis.

Identify Solution Types: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.

Solve Complex Equations: Solve linear equations with rational number coefficients, including those requiring the distributive property and combining like terms.

• Slope Comparison Task: Compare a distance-time graph to a distance-time equation to determine which moving object has a greater unit rate.

• Equation Classification Quiz: Categorize a series of equations based on their number of solutions and transform given equations into simpler forms (e.g., x = a or a = b).