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North CarolinaMaths

Linear Equations and Functions

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you turn a real situation into an equation or inequality you can solve?

Create linear, quadratic, and exponential equations and inequalities in one or two variables to model and solve problems (NC.M1.A-CED.1, A-CED.2).
An NC Math 1 EOC answer on creating equations and inequalities (NC.M1.A-CED.1, A-CED.2): defining the variable, translating rates and fixed amounts, choosing the right inequality symbol, and judging viability.
11 min answer →

How do you graph a linear equation, and how do you read its intercepts and slope from the graph?

Graph linear equations in two variables and identify slope and intercepts, labeling axes and scale (NC.M1.A-CED.2, F-IF.4).
An NC Math 1 EOC answer on graphing linear equations (NC.M1.A-CED.2, F-IF.4): plotting from slope-intercept form, finding x- and y-intercepts, graphing from standard form, and reading slope from a graph.
10 min answer →

How do you rearrange a formula to solve for a different variable?

Rearrange formulas and literal equations to isolate a specified variable (NC.M1.A-CED.4).
An NC Math 1 EOC answer on literal equations (NC.M1.A-CED.4): treating other letters as constants, undoing operations in reverse, clearing fractions, and dividing the whole opposite side.
9 min answer →

How do you find slope, and how do you write the equation of a line from the information given?

Find slope and write linear functions in slope-intercept and point-slope form from a graph, a description, or two points (NC.M1.F-LE.2, F-BF.1a).
An NC Math 1 EOC answer on slope and writing linear equations (NC.M1.F-LE.2, F-BF.1a): the slope formula, slope-intercept and point-slope forms, and building a line from two points or a context.
11 min answer →

How do you solve a linear equation in one variable, and how does each step follow from the properties of equality?

Solve linear equations in one variable, including those with letter coefficients, and justify each step from the properties of equality (NC.M1.A-REI.1, A-REI.3).
An NC Math 1 EOC answer on solving linear equations (NC.M1.A-REI.1, A-REI.3): the properties of equality, clearing fractions, variables on both sides, and recognizing no-solution and identity cases.
10 min answer →

How do you solve a linear inequality, and when does the inequality sign flip?

Solve linear inequalities in one variable and represent the solution on a number line, applying the sign-flip rule for negatives (NC.M1.A-REI.3).
An NC Math 1 EOC answer on solving linear inequalities (NC.M1.A-REI.3): the same routine as equations plus the flip rule for negatives, open and closed circles, and graphing the solution ray.
10 min answer →