Lesson 3.8 – Rewriting Equations and formulas
If we look at the equations:
We notice that it is in the form
some number
some number
some number
Since the numbers can change, we write the general form as:
General Form :
where all the coefficients and constants have been replaced with letters. This is called a literal equation.
We can use the literal form to solve for the variable by rearranging the equation and then inserting the
numbers in for the letters.
Ex.
Solve
for . Then use the solution to solve
Step 1: Rearrange to solve for x
Step 2: Use the solution to solve
So the solution of
is 3.
Remember that the solution to an equation is a number that makes the equation true.
If we had solved the equation the way we had learned before, we would get the same solution.
Pair Check:
Solve
for x. Then find the solution for
When we have equations that have two or more variables, we can rewrite it so that one variable is a function
of the other variable.
Ex:
rewrite so that
is a function of .
Ex:
rewrite so that
is a function of .
Next we will rewrite formulas to isolate different variables. We do this because it is usually easier to rearrange
the formula before the numbers have been substituted into the formula.
Ex: the distance formula is given by
where:
distance
rate
time
The way the equation is set up now, we are solving for the distance. But what if we have the distance and we
want to find the time it takes to travel that distance?
Ex:
The area of a triangle is given by the formula
Where b is the base and h is the height.
a) Solve the formula for the height
b) Use the rewritten formula to find the height of a triangle with a base that is 14 meters long and an area
of 64.4 square meters.
Pair check:
The area of a rectangle is
where is the length and
is the width.
a) Solve the formula for the length
b) Use the rewritten formula to find the length of a triangle with an area of 351 cm 2 and a width of 13 cm.
What happens when you are given the temperature in degrees Celsius? (I panic because I only understand
degrees Fahrenheit)
If we know that
we can rearrange the formula so that F is a function of C.
If we know that the temp is 14°C, what is it in degrees F?
If the temp is 10° C, what is the temp in degrees F?