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OhioMaths

Linear Equations and Inequalities

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 word problem into an equation or inequality, define the variable, and solve it to answer the question?

Create equations and inequalities in one variable from a real-world context and use them to solve problems (Ohio A-CED.1).
An Ohio Algebra I answer on creating equations and inequalities from context (A-CED.1): defining a variable, translating phrases into symbols, building the model, and interpreting the answer in the situation.
11 min answer →

How do you rearrange a formula to solve for a different variable, treating every other letter as a constant?

Rearrange literal equations and formulas to highlight a quantity of interest, using the same reasoning as solving an equation (Ohio A-CED.4, A-REI.3).
An Ohio Algebra I answer on rearranging formulas (A-CED.4): solving for a chosen variable, treating the other letters as constants, and applying inverse operations such as dividing or taking a root.
11 min answer →

What does slope measure, how do you read the intercepts, and how do you graph a line from its equation?

Interpret slope as a rate of change, find the x- and y-intercepts, and graph a line from slope-intercept form (Ohio F-IF.6, A-REI.10).
An Ohio Algebra I answer on slope and graphing lines (F-IF.6, A-REI.10): slope as rise over run and as a rate of change, finding intercepts, and graphing from slope-intercept form.
11 min answer →

How do you solve a linear equation in one variable, including ones with variables on both sides, and what does it mean when an equation has no solution or infinitely many?

Solve linear equations in one variable, including those with variables on both sides and with the distributive property, and recognize no-solution and identity cases (Ohio A-REI.3, A-REI.1).
An Ohio Algebra I answer on solving linear equations (A-REI.3): clearing parentheses and fractions, collecting variables on one side, and recognizing equations with no solution or infinitely many solutions.
11 min answer →

How do you solve a linear inequality, when do you flip the inequality sign, and how do you show the solution on a number line?

Solve linear inequalities in one variable, flip the inequality when multiplying or dividing by a negative, and represent the solution as an interval and on a number line (Ohio A-REI.3).
An Ohio Algebra I answer on solving linear inequalities (A-REI.3): the flip rule when multiplying or dividing by a negative, graphing on a number line with open and closed dots, and interpreting the solution set.
11 min answer →

How do you write the equation of a line from a slope and a point, from two points, or from a graph, and when do you use slope-intercept versus point-slope form?

Write the equation of a line in slope-intercept and point-slope form from a slope and point, two points, or a graph (Ohio A-CED.2, F-IF, F-LE).
An Ohio Algebra I answer on writing equations of lines (A-CED.2): using slope-intercept and point-slope form, finding slope from two points, and writing parallel and perpendicular lines.
12 min answer →