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Objectives
Objectives
Algebraically solve linear functions
Solve word problems that use linear function
Algebraically Solving Linear Functions
Algebraically Solving Linear Functions
Linear functions are used to model many types of real-world phenomena, therefore learning to solve linear functions will help you find answers to many life situations. To begin, let's solve some generic problems before jumping into applications.
Ex 1: Consider the linear function:
Ex 1: Consider the linear function:
f (x) = 5x + 75, when will f (x) = 125?
f (x) = 5x + 75, when will f (x) = 125?
First start by replacing f (x) in the linear function with 125:
Next, since our goal is to isolate the variable x move
any constants away from the x-term to the other side
of the equation.
The next step is to get the coefficient of x to equal positive
one, so we divide both sides by 5.
Finally, our answer is 10 = x, which we can rewrite as x = 10.
First start by replacing in the linear function with 15:
Next, let’s isolate the x–variable x by moving 80 to the opposite side of the equation.
The next step is to get the coefficient of x to equal positive one, so we multiply both sides by –2.
Finally, our answer is 130 = x, which we can rewrite as x = 130.
First calculate the slope using the formula:
Next, choose one of the known points along with the slope and plug into
the slope–intercept formula, then solve for b.
The next step is to write the complete function: f (x) = –2x + 10
Finally, set f (x) = 0 and solve for x. –2x + 10 = 0 results in x = 5.
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