**Colorado Academic Education Standards (CAS)**. Linear equations are equations that have two variables and when graphed are a straight line. Linear equation can be graphed based on their slope and y-intercept. The standard equation for a line is y = mx + b, where m is the slope and b is the y-intercept. Slope can be found with the formula m = (y2 - y1)/(x2 - x1), which represents the change in y over the change in x. Read More...

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Linear equationsWorksheet/Answer key

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CO.8.2. Patterns, Functions, and Algebraic Structures

8.2.1. Linear functions model situations with a constant rate of change and can be represented numerically, algebraically, and graphically. Students can:

8.2.1.a. Describe the connections between proportional relationships, lines, and linear equations. (CCSS: 8.EE)

8.2.1.b. Graph proportional relationships, interpreting the unit rate as the slope of the graph. (CCSS: 8.EE.5)

8.2.1.d. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. (CCSS: 8.EE.6)

8.2.1.e. Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. (CCSS: 8.EE.6)

8.2.3. Graphs, tables and equations can be used to distinguish between linear and nonlinear functions. Students can:

8.2.3.a. Define, evaluate, and compare functions. (CCSS: 8.F)

8.2.3.a.iv. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. (CCSS: 8.F.3)

8.2.3.b. Use functions to model relationships between quantities. (CCSS: 8.F)

8.2.3.b.ii. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. (CCSS: 8.F.4)

8.2.3.b.v. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. (CCSS: 8.F.5)

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