Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# 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 line… 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.