Rearranging Equations of Lines

Multiple Select

Select the algebraic expressions that are equivalent to:

$$\left(4y\right)\left(3x\right)\left(-2xy\right)^{-2}$$  

• $$\frac{12xy}{4x^2y^2}$$  

• $$\frac{3}{xy}$$  

• $$-24x^2y^2$$  

• $$6xy\left(xy\right)^{-2}$$  

• 25

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​Rearranging Equations of Lines

By: Mr. Aronoff (For this lesson, you will need a partner)

Guided Instruction - Different Forms of Linear Equations

Three linear equations and their graphs
are shown.

1.Discuss with your partner what you
notice about the graphs and
equations.

Summarize your discussion.

Open Ended

Discuss with your partner what you notice about the graphs and equations.

The equations of the lines can be written in different but equivalent forms. Each form of the equation relates to different features on the graph of the relationship, including the slope, y-intercept, and other points on the line.

One form for the equation of a line is the Slope-Intercept Form.

2. Discuss with your partner why
this form is called Slope-Intercept
form. Summarize your discussion.

Open Ended

Discuss with your partner why this form is called Slope-Intercept form. Summarize your discussion.

A second form for the equation of a line is called Point-Slope form. Point-Slope form can be written using the slope and any point on the line.

3. Compare the equation and the
graph of the line. What do you
notice about the signs of the
coordinates of the green point used
to write the equation compared to
the values in the equation?

Open Ended

3. Compare the equation and the graph of the line. What do you notice about the signs of the coordinates of the green point used to write the equation compared to the values in the equation?

The third form for the equation of a line is called Standard Form.

5. Rewrite the equation
in Slope-Intercept form by isolating the
variable, y.

Draw

Rewrite the equation in slope-intercept form by isolating the variable y. Show your work to receive credit:

$$3x+4y=8$$  

Guided Practice - Rewriting Equations of Lines in
Different Forms

1.

Use the equation to complete the following.

a.

What is the form of the linear equation given?

b. Rewrite the equation in Standard Form.

Open Ended

What is the form of the equation given?

$$f\left(x\right)=\frac{2}{5}x-4$$  

Draw

Rewrite the equation in standard form. Show your work to receive credit:

$$f\left(x\right)=\frac{2}{5}x-4$$  

2. Use the equation to complete the following.

a.

What is the form of the linear equation given?

b.

Rewrite the equation in Standard Form.

Fill in the Blank

What is the form of the equation of a line given?

$$\left(y-7\right)=-\frac{1}{3}\left(x+2\right)$$  

Draw

Rewrite the equation in standard form. Show your work to receive credit:

$$\left(y-7\right)=-\frac{1}{3}\left(x+2\right)$$  

3. Use the equation to complete the following.

a.

What is the form of the linear equation given?

b.

Rewrite the equation in Slope-Intercept Form.

Fill in the Blank

What is the form of the equation of a line given?

$$6x-9y=12$$  

Draw

Rewrite the equation in slope-intercept form. Show your work to receive credit:

$$\left(y-7\right)=-\frac{1}{3}\left(x+2\right)$$  

Open Ended

Complete the following sentence: Today, I was a little confused about...