Section 2.6

Using and Rearranging Formulas

2.6 Lecture Guide: Using and Rearranging Formulas

To solve a linear equation for a specified variable, we want to isolate that variable on one side of the equation with all other variables on the other side of the equation. This process involves the same steps used to solve a linear equation in one variable. If there is more than one variable in the equation, it is helpful to think of all variables as constants except the variable you are solving for.

Objective: Rewrite a linear equation in the form

Solve each equation below for y, and write it in the form . y mx b

y mx b

1. 3 2 12x y

and calculate the x- and y-intercepts of the graph of a linear equation.

2. 5 6 30x y

Solve each equation below for y, and write it in the form . y mx b

3. 8 2 10x y

Solve each equation below for y, and write it in the form . y mx b

4. 13 4

x y

Solve each equation below for y, and write it in the form . y mx b

5. 1.5 0.3 1.2x y

Solve each equation below for y, and write it in the form . y mx b

6. 3 2 2 5 3 12x y x y

Solve each equation below for y, and write it in the form . y mx b

Algebraically Finding the x- and y-interceptsIn Section 2.2, we introduced x- and y-intercepts. Recall that the x-intercept is the point on the graph of a line where that line crosses the x-axis. This is the point with a y-coordinate of ______. The y-intercept is the point on the graph of a line where that line crosses the y-axis. This is the point with an x-coordinate of ______.

So if we have a linear equation in two variables, we can algebraically find the x-intercept by substituting ______ for the y variable and solving for x. Similarly, we can algebraically find the y-intercept by substituting ______ for the x variable and solving for y.

Algebraically find the x- and y-intercepts for the graphs of the following equations. To check your work use a graphing calculator to create a graph and a table for each equation.

3 4 12x y 7.x-intercept:

y-intercept:

8.2

43

y x

x-intercept:

y-intercept:

Algebraically find the x- and y-intercepts for the graphs of the following equations. To check your work use a graphing calculator to create a graph and a table for each equation.

9. 2 3y x x-intercept:

y-intercept:

Algebraically find the x- and y-intercepts for the graphs of the following equations. To check your work use a graphing calculator to create a graph and a table for each equation.

10. A young entrepreneur operating a gum ball machine has a fixed monthly overhead cost of $5. He makes a profit of $0.20 on each gum ball sold.

(a) Write an equation that gives the monthly profit for this business when x gum balls are sold in a month.

(b) Using the equation from part (a), determine the x-intercept of the graph of this equation and interpret this point.

10. A young entrepreneur operating a gum ball machine has a fixed monthly overhead cost of $5. He makes a profit of $0.20 on each gum ball sold.

(c) Using the equation from part (a), determine the y-intercept of the graph of this equation and interpret this point.

Objective: Solve an equation for a specified variable.

1

2A bh

Solve each equation for the specified variable.

11. for b

Solve each equation for the specified variable.

1 1 2 2PV PV 1P12. for

Solve each equation for the specified variable.

2 2P l w 13. for l

1

2A h a b

Solve each equation for the specified variable.

14. for a

y mx b

Solve each equation for the specified variable.

15. for x

2 4 2 6m t a m

Solve each equation for the specified variable.

16. for m