FreeAlgebra                             Tutorials!

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:

# Graphing Linear Equations in the Coordinate Plane

## Graphing a Linear Equation

The solution set to an equation in two variables consists of all ordered pairs that satisfy the equation. For example, the solution set to y = 2x + 3 can be written in set notation as {(x, y) | y = 2x + 3}. However, this set notation does not shed any light on the solution set to y = 2x + 3. We can get a better understanding of the solution set with a visual image or graph of the solution set.

Example

Graphing a linear equation

Graph the solution set to y = 2x + 3.

Solution

If we arbitrarily choose x = -4, then y is determined by the equation y = 2x + 3:

y = 2(-4) + 3 = -5

So the ordered pair (-4, -5) satisfies the equation. In this manner we can make the following table of ordered pairs:

 x -4 -3 -2 -1 0 1 y = 2x + 3 -5 -3 -1 1 3 5

Plot these ordered pairs as shown in the figure below. Of course, there are infinitely many ordered pairs that satisfy y = 2x + 3, but they all lie along the line in the figure below. The arrows on the ends of the line indicate that it extends without bound in both directions. The line in this figure is a graph of the solution set to y = 2x + 3.

In an equation such as y = 2x + 3 the value of y depends on the value of x. So x is the independent variable and y is the dependent variable. Because the graph of y = 2x + 3 is a line, the equation is a linear equation.

 All Right Reserved. Copyright 2005-2019