Section 2.6: Calculating Intercepts and Rearranging Formulas Worksheet 2.6
Recall: What is an intercept?
Question: How do we find intercepts algebraically?
Example: Find the $x$ and $y$-intercept of the line $\frac{x}{2}+\frac{y}{8}=-1$.
Formulas: Formulas express an relationship between one or more variables.
Examples:
$A=\frac{1}{2}bh$
$F=\frac{GMm}{r^2}$
$V=\frac{1}{3}\pi r^2 h$
$F=\frac{9}{5}C+32$
Solving Formulas for a Specified Variable.
Example: Solve the formula for a trapezoid $A=\frac{1}{2}(b_1+b_2)h$ for $b_2$.
Solving Linear Equations for $y$.
Example: Solve the linear equation $3x+2y=5$ for $y$.
Advantage: The "$y=$" version is easier to graph and work with.
Application: owns an ice cream shop in Columbia which has daily overheard costs of $\$$120. The shop makes $\$$2.00 on every item sold. Write an equation which that gives the profit $y$ for this business when it sells $x$ items. Find and interpret the intercepts.
Application: A loan shark gives simple interest loans at a weekly rate of 16 percent. If after 5 weeks the loan shark collects a vig (the amount of interest made) of $\$$28.80, what was the principal amount of the loan? Round your answer to the nearest cent.