Linear Equations

What is a Linear Equation?

An equation whose graph is a line.

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.

Multiple Choice

What is our slope?

y = mx + b

• y

• m

• x

• b

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. 

Multiple Choice

What is our y-intercept?

y = mx + b

• y

• m

• x

• b

Multiple Choice

Which of the following shows a linear equation?

A linear equation can be shown 3 ways:

• xy table

• graph

• equation

Multiple Choice

What is the x-intercept of the graph?

• (5,0)

• (0,5)

• (0,4)

• (4,0)

Multiple Choice

What is the y-intercept?

• (0,15)

• (3,0)

• (15,0)

• (0,3)

Multiple Choice

What is the x-intercept?

• (-2,0)

• (0-6)

• (0,-2)

• (-6,0)

Multiple Choice

What is the y-intercept?

• (2,0)

• (0,2)

• (0,-2)

• (-2,0)

Graphing an Equation

You need only 2 points to graph a line. You can choose a value for x, and then evaluate for y.

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

Evaluating Linear Equations

What does it mean to evaluate?

Evaluating Linear Equations

• Replace the variable with its value

• Follow the Order of Operations

• You will find the answer - the value of the whole equation

Fill in the Blank

If x = 2, in the equation y = 3x - 5, what is the value of y?

Fill in the Blank

If x = 0, in the equation y = -2x - 4, what is the value of y?

Fill in the Blank

If x = -2, in the equation y = -3x - 10, what is the value of y?

Fill in the Blank

If x = -6, in the equation y = 5x + 7, what is the value of y?

Fill in the Blank

If x = 4, the the equation x + y = -12, what is the value of y?

Fill in the Blank

If x = -3, the the equation -2x + y = 15

Fill in the Blank

If x = 4, the equation y = -5x, what is the value of y?

Fill in the Blank

If x = 5, the the equation 5x + y = 20, what is the value of y?

Fill in the Blank

If x = 1, in the equation x + 3y = 10, what is the value of y?