Module 4: Linear equations

Topic A: Writing and solving linear equations

Learn

Intro to equations with variables on both sides
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Equations with variables on both sides: 20-7x=6x-6
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Equation with variables on both sides: fractions
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Equation with the variable in the denominator
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Equations with parentheses
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Number of solutions to equations
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Worked example: number of solutions to equations
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Creating an equation with no solutions
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Creating an equation with infinitely many solutions
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Practice

Equations with variables on both sidesGet 3 of 4 questions to level up!
Equations with variables on both sides: decimals & fractionsGet 3 of 4 questions to level up!
Equations with parenthesesGet 3 of 4 questions to level up!
Equations with parentheses: decimals & fractionsGet 3 of 4 questions to level up!
Number of solutions to equationsGet 3 of 4 questions to level up!
Number of solutions to equations challengeGet 3 of 4 questions to level up!

Topic B: Linear equations in two variables and their graphs

Learn

Rates & proportional relationships example
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Rates & proportional relationships: gas mileage
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Graphing proportional relationships: unit rate
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Graphing proportional relationships from a table
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Graphing proportional relationships from an equation
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Points on the coordinate plane examples
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Testing solutions to linear equations
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Graphing a linear equation: 5x+2y=20
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Practice

Rates & proportional relationshipsGet 5 of 7 questions to level up!
Graphing proportional relationshipsGet 3 of 4 questions to level up!
Solutions to 2-variable equationsGet 3 of 4 questions to level up!
Complete solutions to 2-variable equationsGet 3 of 4 questions to level up!

Topic C: Slope and equations of lines

Learn

x-intercept of a line
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Intercepts from a table
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Intercepts from an equation
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Worked example: intercepts from an equation
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Slope & direction of a line
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Intro to slope
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Slope formula
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Worked example: slope from graph
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Slope of a line: negative slope
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Worked example: slope from two points
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Slope of a horizontal line
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Converting to slope-intercept form
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Proving slope is constant using similarity
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Intro to point-slope form
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Intro to slope-intercept form
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Graph from slope-intercept equation
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Slope-intercept equation from graph
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Slope-intercept equation from slope & point
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Slope-intercept equation from two points
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Slope-intercept form from a table
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Slope-intercept form problems
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Practice

Intercepts from a graphGet 3 of 4 questions to level up!
Intercepts from an equationGet 3 of 4 questions to level up!
Slope from graphGet 3 of 4 questions to level up!
Slope from two pointsGet 3 of 4 questions to level up!
Slope-intercept introGet 3 of 4 questions to level up!
Slope from equationGet 3 of 4 questions to level up!
Graph from slope-intercept formGet 3 of 4 questions to level up!
Slope-intercept equation from graphGet 3 of 4 questions to level up!
Slope-intercept from two pointsGet 3 of 4 questions to level up!

Topic D: Systems of linear equations and their solutions

Learn

Systems of equations: trolls, tolls (1 of 2)
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Systems of equations: trolls, tolls (2 of 2)
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Testing a solution to a system of equations
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Systems of equations with graphing
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Systems of equations with graphing
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Systems of equations with graphing: 5x+3y=7 & 3x-2y=8
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Systems of equations with graphing: y=7/5x-5 & y=3/5x-1
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Systems of equations with graphing: chores
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Systems of equations with elimination: 3t+4g=6 & -6t+g=6
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Systems of equations with elimination
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Systems of equations with elimination: x+2y=6 & 4x-2y=14
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Systems of equations with elimination: -3y+4x=11 & y+2x=13
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Systems of equations with elimination: 2x-y=14 & -6x+3y=-42
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Systems of equations with elimination: 4x-2y=5 & 2x-y=2.5
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Systems of equations with elimination: x-4y=-18 & -x+3y=11
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Systems of equations with elimination: 6x-6y=-24 & -5x-5y=-60
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Systems of equations with substitution: 2y=x+7 & x=y-4
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Systems of equations with substitution
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Systems of equations with substitution: y=4x-17.5 & y+2x=6.5
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Systems of equations with substitution: -3x-4y=-2 & y=2x-5
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Systems of equations with substitution: 9x+3y=15 & y-x=5
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Systems of equations with substitution: y=-5x+8 & 10x+2y=-2
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Systems of equations with substitution: y=-1/4x+100 & y=-1/4x+120
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Systems of equations with elimination: apples and oranges
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Systems of equations with elimination: TV & DVD
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Systems of equations with elimination: King's cupcakes
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Systems of equations with elimination: Sum/difference of numbers
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Systems of equations with elimination: potato chips
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Systems of equations with elimination: coffee and croissants
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Systems of equations with substitution: coins
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Systems of equations with substitution: potato chips
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Systems of equations with substitution: shelves
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Age word problem: Imran
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Age word problem: Ben & William
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Age word problem: Arman & Diya
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Solutions to systems of equations: consistent vs. inconsistent
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Systems of equations number of solutions: fruit prices (1 of 2)
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Systems of equations number of solutions: fruit prices (2 of 2)
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Systems of equations number of solutions: y=3x+1 & 2y+4=6x
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Solutions to systems of equations: dependent vs. independent
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Number of solutions to a system of equations graphically
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Forming systems of equations with different numbers of solutions
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Comparing Celsius and Fahrenheit temperature scales
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Converting Fahrenheit to Celsius
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Practice

Solutions of systems of equationsGet 3 of 4 questions to level up!
Systems of equations with graphingGet 3 of 4 questions to level up!
Systems of equations with eliminationGet 3 of 4 questions to level up!
Systems of equations with elimination challengeGet 3 of 4 questions to level up!
Systems of equations with substitutionGet 3 of 4 questions to level up!
Linear systems of equations capstoneGet 4 of 5 questions to level up!
Systems of equations word problemsGet 3 of 4 questions to level up!
Age word problemsGet 3 of 4 questions to level up!
Number of solutions to a system of equations graphicallyGet 3 of 4 questions to level up!
Number of solutions to a system of equations algebraicallyGet 5 of 7 questions to level up!

About this unit

"In Module 4, students use similar triangles learned in Module 3 to explain why the slope of a line is well-defined. Students learn the connection between proportional relationships, lines, and linear equations as they develop ways to represent a line by different equations (y = mx + b, y – y1 = m, etc.). They analyze and solve linear equations and pairs of simultaneous linear equations. The equation of a line provides a natural transition into the idea of a function explored in the next two modules." Eureka Math/EngageNY (c) 2015 GreatMinds.org