## MTH 5 - Bundle 4-5 - First Degree Equations and Inequalities and Systems of Linear Equations at Danville Community College

### Course Description

Effective: 2017-08-01

Includes solving first degree equations and inequalities containing one variable, and using them to solve application problems. Emphasizes applications and problem solving. Includes finding the equation of a line, graphing linear equations and inequalities in two variables and solving systems of two linear equations. Emphasizes writing and graphing equations using the slope of the line and points on the line, and applications. Credit is not applicable toward graduation.

Lecture 2 hours. Total 2 hours per week.

2 credits

### General Course Purpose

To prepare students for successful entry into credit mathematics courses as well as other credit courses requiring basic math competencies as prerequisites.

### Course Prerequisites/Corequisites

Prerequisites: MTE 1-3 or qualifying placement score

### Course Objectives

- Equations and Inequalities
- Solve first degree equations in one variable using the Addition and/or Multiplication Property of Equality.
- Solving Linear Equations in One Variable that contain parentheses and/or the variable on both sides of the equal sign.
- Solve first degree equations in one variable and identify the solution to an equation as finite, the empty set or all real numbers.
- Solve application problems using a single first degree equation or inequality.
- Solve a formula or equation for one of its variables using the Addition and/or Multiplication Property of Equality.
- Solve first degree inequalities in one variable stating the solution using inequality notation.
- Solve first degree inequalities in one variable and graph the solution on a real number line.
- Solve first degree absolute value equations containing a single absolute value.
- Graphing
- Determine the coordinates of a point plotted on the coordinate plane.
- Graphing Linear Equations in Two Variables
- Identify the x and y intercepts of a graph.
- Graph a linear equation by plotting intercepts.
- Graph a horizontal and vertical line given its equation.
- Find the slope of a line given two points on the line.
- Find the slope of a line given its graph.
- Find the slope of horizontal and vertical lines.
- Write an equation of a line in slope-intercept form given the slope and the y-intercept.
- Use point-slope form to write an equation of a line in slope intercept form given the slope and a point on the line.
- Use point-slope form to write an equation of a line in slope intercept form given two points on the line.
- Find the equation of a line that is parallel or perpendicular to a given line and passes through a given point.
- Write the equation of a vertical line and horizontal line.
- Find the slope of a line given its equation in slope-intercept form.
- Find the slope of a line given its equation by converting to slope-intercept form.
- Graph a linear inequality in two variables.
- Solve Systems of Linear Equations by Graphing
- Determine if an ordered pair is a solution of system of equations in two variables.
- Graph a linear equation by finding and plotting ordered pair solutions.
- Graph an equation given in slope-intercept form.
- Solve systems of linear equations by graphing, substitution, and elimination. Identify a system of linear equations as consistent and independent, consistent and dependent, or inconsistent.
- Solve applications problems that require linear equations, inequalities and systems of linear equations in two variables.
- Identify independent and dependent variables.
- Evaluate y = f(x) for specific values of x.
- Given the graph of y = f(x), evaluate f(x)
- Given the graph of y = f(x), find x for specific values of f(x).

### Major Topics to be Included

- Solving and Graphing First Degree Equations
- Solving and Graphing First Degree Inequalities
- Solving Systems of Equations