Graphing Linear Equations

Linear Equations are most often expressed in one of three forms:

Forms of Linear Equations

Linear Equations are most often expressed in one of three forms: Slope-Intercept Form: ,

Forms of Linear Equations

Linear Equations are most often expressed in one of three forms: Slope-Intercept Form: , Point-Slope Form: , and

Forms of Linear Equations

Linear Equations are most often expressed in one of three forms: Slope-Intercept Form: , Point-Slope Form: , and Standard Form: .

Forms of Linear Equations

Linear Equations are most often expressed in one of three forms: Slope-Intercept Form: , Point-Slope Form: , and Standard Form: .

Each form allows for quick and easy ways to graph the line they represent.

Forms of Linear Equations

One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form ().The steps are:

Make a Table

One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form ().The steps are:1. Assign a value to the x-variable,

Make a Table

One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form ().The steps are:1. Assign a value to the x-variable,2. Calculate the corresponding value for the

y-coordinate, and

Make a Table

One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form ().The steps are:1. Assign a value to the x-variable,2. Calculate the corresponding value for the

y-coordinate, and3. Repeat.

Make a Table

One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form ().The steps are:1. Assign a value to the x-variable,2. Calculate the corresponding value for the

y-coordinate, and3. Repeat.In this way, we can create a table of ordered pairs and plot them on the coordinate plane.

Make a Table

Consider the equation .

Make a Table

-2

Consider the equation .

Make a Table

-2 𝑦=12(−𝟐)+2 =1

Consider the equation .

Make a Table

-2 𝑦=12(−𝟐)+2 (-2,1)=1

Consider the equation .

Make a Table

-2

0

𝑦=12(−𝟐)+2

𝑦=12(𝟎)+2

(-2,1)=1

=2 (0, 2)

Consider the equation .

Make a Table

-2

0

2

𝑦=12(−𝟐)+2

𝑦=12(𝟎)+2

𝑦=12(𝟐)+2

(-2,1)=1

=2 (0, 2)

=3 (2, 3)

Another method for graphing lines when an equation is in slope-intercept form is as follows:

Use the slope and intercept

Another method for graphing lines when an equation is in slope-intercept form is as follows:1. Plot the y-intercept on the coordinate

plane; that's the point (0, b).

Use the slope and intercept

Another method for graphing lines when an equation is in slope-intercept form is as follows:1. Plot the y-intercept on the coordinate

plane; that's the point (0, b).2. Use the slope to find another point (and

repeat).

Use the slope and intercept

Another method for graphing lines when an equation is in slope-intercept form is as follows:1. Plot the y-intercept on the coordinate

plane; that's the point (0, b).2. Use the slope to find another point (and

repeat).3. Draw a line through the points.

Use the slope and intercept

1. Plot the y-intercept

Consider the equation .

Use the slope and intercept

(0, b) = (0, 7)

1. Plot the y-intercept

2. Use the slope to find another point (and repeat).

Consider the equation .

Use the slope and intercept

(0, b) = (0, 7)

From the intercept, move down 5 and right 4 (or up 5 and left 4).

1. Plot the y-intercept

2. Use the slope to find another point (and repeat).

3. Draw a line through the points.

Consider the equation .

Use the slope and intercept

(0, b) = (0, 7)

From the intercept, move down 5 and right 4 (or up 5 and left 4).

This method is very similar to the slope-intercept method. To graph a line using this method, do the following:

Use a point and the slope

This method is very similar to the slope-intercept method. To graph a line using this method, do the following:1. Plot the point (, ).

Use a point and the slope

This method is very similar to the slope-intercept method. To graph a line using this method, do the following:1. Plot the point (, ).2. Use the slope to find another point (and

repeat).

Use a point and the slope

This method is very similar to the slope-intercept method. To graph a line using this method, do the following:1. Plot the point (, ).2. Use the slope to find another point (and

repeat).3. Draw a line through the points.

Use a point and the slope

1. Plot the point (, )

Consider the equation .

Use a point and the slope

(, )= (-3, 2)

1. Plot the point (, )

2. Use the slope to find another point (and repeat).

Consider the equation .

Use a point and the slope

(, )= (-3, 2)

From (-3, 2), move up 7 and right 3 -– or down 7 and left 3.

1. Plot the point (, )

2. Use the slope to find another point (and repeat).

3. Draw a line through the points.

Consider the equation .

Use a point and the slope

(, )= (-3, 2)

From (-3, 2), move up 7 and right 3 -– or down 7 and left 3.

This method is used when the line is in Standard Form ().

Use the Intercepts

This method is used when the line is in Standard Form (). 1. The x-intercept is easily calculated by

setting y to 0 and solving for .

Use the Intercepts

This method is used when the line is in Standard Form (). 1. The x-intercept is easily calculated by

setting y to 0 and solving for .2. The y-intercept is calculated by setting to

zero and solving for .

Use the Intercepts

This method is used when the line is in Standard Form (). 1. The x-intercept is easily calculated by

setting y to 0 and solving for .2. The y-intercept is calculated by setting to

zero and solving for .3. Plot the two intercepts and draw a line

through them.

Use the Intercepts

1. Set and solve for .

Consider the equation .

Use the Intercepts

;

1. Set and solve for .

2. Set and solve for .

Consider the equation .

Use the Intercepts

;

;

1. Set and solve for .

2. Set and solve for .

3. Draw a line through the points.

Consider the equation .

Use the Intercepts

;

;