WHAT ARE LINEAR EQUATIONS?

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has a variable whose exponent is more than 1. The graph of a linear equation always forms a straight line.

Linear Equation Definition: A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear' equation.

There are linear equations in one variable and linear equations in two variables. Let us learn how to identify linear equations and non-linear equations with the help of the following examples.

WHAT ARE LINEAR EQUATIONS?

Linear Equations

Graphing Linear Equations

Linear Graph

• An equation whose graph is a line is a linear equation.

• You can plot points on a coordinate plane to graph a linear equation.

• Example: y = -4x + 4.

Linear Equations Review

Slope-Intercept Form

Point-Slope Form

Standard Form

Parallel & Perpendicular Lines

X and Y Intercepts

• Linear equations have x and y-intercepts. 

• The x-intercept is the x-coordinate of the point at which the graph crosses the x-axis.

• The y-intercept is the y-coordinate of the point at which the graph crosses the y-axis. 

Slope-Intercept: y = mx+b

• Used for graphing linear equations

• Need a slope (m) and y-intercept (b)

Point-slope Form: y - y₁ = m( x - x₁)

• Useful when you are given a point (x₁, y₁) and slope (m)

• Plug in the opposite values of points into formula

Graphing an Equation

• You need only 2 points to graph a line.

• You can choose a value for x, and then evaluate for y.

Standard Form : Ax + By = C

• Form is useful to convert to a different form.

• A, B, and C are all whole numbers.

Make a Table of Values or T-Chart

• Choose a value for x, plug in, and solve for y.

• Do this 2 or 3 times.

• Then, use the points to graph your equation.

Build a t-chart

• The Red Arrow shows y=-4 after simplifying.

• The Green Arrow shows y=0 after simplifying.

• The Yellow Arrow shows y=4 after simplifying.

Parallel Lines : Slopes are the same

Perpendicular Lines : Opposite Reciprocal slopes

Use point-slope and then convert to slope-intercept.

Graph

• Plot each ordered pair.

• Connect with a line.

• The points were (0,-4), (2,0), (4,4)