Graphing Linear Equations

Graphing Linear Equations

By Greg Cimenski

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.

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 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

Graph

Plot each ordered pair. Connect with a line.

Fill in the Blanks

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

Fill in the Blanks

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

Fill in the Blanks

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

Fill in the Blanks

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

Multiple Choice

What is our slope?

y = mx + b

• y

• m

• x

• b

Multiple Choice

What is the y-intercept in the equation y= -2x + 5

• -2
• 3
• 5
• Cannot be Determined

Multiple Choice

Find the slope

• 5/2
• -5/2
• 2/5
• -2/5

Multiple Choice

Find the slope

• -5/3
• -3/5
• 5/3
• 3/5

Multiple Choice

What is the simple definition of slope? 

• line
• run/rise
• undefinied
• rise/run

Multiple Choice

Find the slope of the line.

• -2
• 2
• -1
• 1

Multiple Choice

Identify the slope in the equation below.

y = 4x - 10

• y

• 4

• x

• -10

Multiple Choice

Look at the graph.

Does it have a positive or negative slope?

• positive

• negative

Multiple Choice

What is the slope in the picture?

• Positive
• Negative
• Zero
• Undefined

Multiple Choice

What is the slope in the picture?

• Positive
• Negative
• Zero
• Undefined

Multiple Choice

What type of slope?

• negative
• steep
• undefined
• zero slope

Multiple Choice

Find the slope of the line.

• Undefined
• 0
• 1
• -1

Multiple Choice

What type of slope does the graph have?

• positive
• negative
• zero
• undefined

Multiple Choice

Slope is know as rise/

• run
• fall
• none
• rise

Multiple Choice

Which graph has a positive slope?

Multiple Choice

Which graph has a negative slope?

Multiple Choice

Which graph has a zero slope?

Multiple Choice

What is our y-intercept?

y = mx + b

• y

• m

• x

• b

Multiple Select

What is the slope of this graph? rise/run

• m = 2

• m = 3

• m = 2/3

• m = 2/1

Multiple Choice

What is the y-intercept of this graph? rise/run

• b = 2

• b = 3

• b = 0

• b = 3/4

Multiple Choice

What is the linear equation for this graph?

• y = 2x + 0

• y = 1/2x + 2

• y = 0x + 2

• y = x + 0

Multiple Choice

What is the slope of this graph?

• m = 2/3

• m = 1/2

• m = 2/2

• m = 1/4

Multiple Choice

What is the y-intercept of this graph?

• b = 2/3

• b = 2

• b = 3

• b = -2

Multiple Choice

What is the linear equation of this graph?

• y = 1/2x + 2

• y = 2/3x + 3

• y = x + 2

• y = 2/1x + 2

Multiple Select

What is the slope?

• 3/1

• -15/5

• -3/1

• 2/3

Multiple Choice

What is the y-intercept?

• b = 5

• b = -5

• b = 0

• b = -2

Open Ended

Write the linear equation for this graph :)

Graph the Equation using a T-Table:

​

Step One:

Make a T-Table

Always choose at least 3 x-values; then find the corresponding y-values.

Step Two:

Graph each ordered pair in the T-Table on a Coordinate Plane.

-Use a straight edge to draw a line through the points.

-Since the graph of y = x - 4 is a straight line, it is a LINEAR EQUATION.

Multiple Choice

Complete the T-Table for:

y = x + 1

• y = 0, 1, 2

• y = 1, 2, 3

• y = 2, 3, 4

• y = 3, 4, 5

Multiple Choice

Which point is a solution to the equation?

• (1,5)

• (5,1)

• (2,5)

• (4,15)

Multiple Choice

Which equation was used to make the graph?

• y = 3x

• y = 2x

• y = x + 2

• y = x - 2

Fill in the Blanks

Name a point on this linear equation.

Poll

How do you feel about graphing equations?

• Great!

• So-So

• Confused