Linear Equations
Literal Equations
Simplifying Expressions & Solving Equations
Two Equations containing Two Variables
Solving Linear Equations
Plane Curves Parametric Equation
Linear Equations and Matrices
Trigonometric Identities and Conditional Equations
Solving Quadratic Equation
Solving Systems of Linear Equations by Graphing
Exponential and Logarithmic Equations
Quadratic Equations
Homework problems on homogeneous linear equations
Solving Quadratic Equations
Functions, Equations, and Inequalities
Solving Multiple-Step Equations
Test Description for Quadratic Equations and Functions
Solving Exponential Equations
Linear Equations
Linear Equations and Inequalities
Literal Equations
Quadratic Equations
Linear Equations in Linear Algebra
Investigating Liner Equations Using Graphing Calculator
represent slope in a linear equation
Linear Equations as Models
Solving Quadratic Equations by Factoring
Solving Equations with Rational Expressions
Solving Linear Equations
Solve Quadratic Equations by Completing the Square
Solving a Quadratic Equation

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Linear Equations as Models

Big Idea: Linear equations in slope intercept form and in standard form are used to write equations that represent real‐life situations. Graphing will also lead to solving linear systems of equations and inequalities.

Objectives of the Unit:

• Students correctly recognize how rate and value are represented in an equation and a graph.
• Students accurately understand how the standard form of an equation for a line is used to model situations.
• Students correctly change standard form to slope‐intercept form.
• Students describe slopes and write equations for horizontal and vertical lines.
• Students can use two points to write an equation for a line.
• Students can use one point and the slope to write an equation for a line.
• Students can find the point where two lines intersect.
• Students graph linear inequalities on a coordinate plane.
• Students solve problems by writing and graphing systems of inequalities.

Student Outcomes:

M1.1.A Select and justify functions and equations to model and solve problems.
M1.1.B Solve problems that can be represented by linear functions, equations and inequalities.
M1.2.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections
among these representations.
M1.3.B Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear
expression affect their graphs and the relationships they represent.
M1.3.D Write and graph an equation for a line given the slope and the y‐intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations.
M1.3.E Write and solve systems of two linear equations and inequalities in two variables.
M1.3.H Determine the equation of a line in the coordinate plane that is described geometrically, including a line through two given points, a line through a given point parallel to a given line, and a line through a given point perpendicular to a given line.
M1.8.A Analyze a problem situation and represent it mathematically.

Student Learning Outcomes for Integrated 1, Unit 8

    Self Assessment
Outcome: “I can…” Example Starting Getting there Got it!
1. …Write an equation using the slope-intercept form, make a table and a graph from information. Emilee had $950 in her account on Jan. 1, she added $75 each month. Model the situation with a table, graph and slope.      
2. …Show examples of linear growth and linear decay. List the characteristics and slope, and sketch a
Linear Growth & Linear Decay
3. …Write an equation using the
standard form of a linear equation.
Each baseball practice the pitching staff must throw for 20 minutes. Brian can throw 3 fastballs per minute and 2
changeups per minute.

a. Write an equation for this situation.
b. Rewrite the equation in slope‐intercept form.

4. …Find the vertical and horizontal
intercepts of an equation.
Find the vertical and horizontal intercepts of the equation:
y = ‐2x + 2
5. …Write equations and find the slope of vertical and horizontal lines. Write an equation for each line:
a. The points (9,3) and (‐1,3) are on the line…
b. The slope is undefined, and the point (‐1,4) is on the
6. …Write an equation from two
points, and write an equation from
other information.
Two points on a line are (1,‐2) and (5,4). Write an equation for the line. What is the slope of the line? What is the vertical intercept of the line?

The slope of a line is -1/2 and one point on the line is (3,4). Write an equation for this line. What is the vertical intercept of the line?

7. …Graph systems of linear equations. The service charge on a checking account at Columbia Bank is $5 per month plus $.15 per Debit Card withdrawal. The service charge at Frontier Bank is $.25 per Debit Card withdrawal.
a. Write and solve a system of equations to model this situation.
8. …Graph a linear inequality on a
Coordinate Plane.
Graph the inequality: y ≥ ‐x

Graph the inequality:

Graph the inequality: 5y – 3x ≥ 15

9. …Graph a system of inequalities to
answer a situation.
Mr. Goldsberry has $600 to buy helmets and bats for the team. He wants to buy at least 15 helmets and bats. Bats are $45 each and helmets are $35 each. Write and graph a system of inequalities to model the situation.