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Rational Expressions
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Solve Two-Step Equations
Multiply, Dividing; Exponents; Square Roots; and Solving Equations
LinearEquations
Solving a Quadratic Equation
Systems of Linear Equations Introduction
Equations and Inequalities
Solving 2nd Degree Equations
Review Solving Quadratic Equations
System of Equations
Solving Equations & Inequalities
Linear Equations Functions Zeros, and Applications
Rational Expressions and Functions
Linear equations in two variables
Lesson Plan for Comparing and Ordering Rational Numbers
LinearEquations
Solving Equations
Radicals and Rational Exponents
Solving Linear Equations
Systems of Linear Equations
Solving Exponential and Logarithmic Equations
Solving Systems of Linear Equations
DISTANCE,CIRCLES,AND QUADRATIC EQUATIONS
Solving Quadratic Equations
Quadratic and Rational Inequalit
Applications of Systems of Linear Equations in Two Variables
Systems of Linear Equations
Test Description for RATIONAL EX
Exponential and Logarithmic Equations
Systems of Linear Equations: Cramer's Rule
Introduction to Systems of Linear Equations
Literal Equations & Formula
Equations and Inequalities with Absolute Value
Rational Expressions
SOLVING LINEAR AND QUADRATIC EQUATIONS
Steepest Descent for Solving Linear Equations
The Quadratic Equation
Linear equations in two variables
   
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Linear equations in two variables

Example 9
Complete Table 6 with solutions to the equation . Then graph the solutions and show that
they are collinear.

Definition
An equation that can be written in the form Ax + B y = C (not both A and B zero) is called a
linear equation of x and y . The graph of all of the solutions to a linear equation with two
variables is a (straight) line (when graphed in the rectangular coordinate plane).
Three or more points in the plane are collinear (lie on a common line) if and only if they all
satisfy a common linear equation.

Example 10
Complete Table 7 with four solutions to the equation x + 2 y = 6. Then graph the solutions and
show that they are collinear.

Example 11
Complete Table 8 with four solutions to the equation 3 x − 2 y = 6. Then graph the solutions and
show that they are collinear.

Definition
When a line or a curve is drawn in the xy-plane, any point on the line or curve that also lies on the
y-axis is called a y-intercept and any point on the line or curve that also lies on the x-axis is
called an x-intercept .
x-intercept: (x,0) y-intercept: (0, y)

Example 12
State all of the intercepts of the curve shown in Figure 9.

   

Example 13
Find the intercepts of the line with equation 3x − 5 y = − 20 .

Example 14
Plot the line 2 x + 4 y = − 8 onto Figure 10 after first finding the intercepts of the line. Find a
third point on your plotted line and show that it also satisfies the equation.

Example 15
Plot onto Figure 11 several points in the xy-plane that satisfy the equation x = − 4 . What do you
observe? What are the intercepts of the resultant curve?

Example 16
What is an equation for the line in Figure 12? What are the intercepts of the line?

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