Writing a Function Rule

Write a Linear Function Rule

Learn how to write a linear function from a linear relationship.

Write a Linear Function Rule

The cost to make 4 bracelets is shown in the table. How can you determine the cost to make any number of bracelets?

Step 1: Examine the relationship between the values in the table. The relationship is Linear (cost

 $\div$ number of bracelets is a constant rate of change of 15) 

Write a Linear Function Rule Continued...

Step 2: Write the function using slope-intercept form

f(x) = mx + b

f(x) = 15x + b

Step 3: Find the value of b. Use any ordered pair from the table ex) (1,17). When x = 1, y = 17

f(1) = 15(1) + b

17 = 15 + b

-15 -15

2 = b

You can use the function  f(x) = 15x + 2 to determine the cost to make any number of bracelets. 

The function 𝘧(𝘹)=𝟣𝟧𝘹+𝟤 is a linear function because the rule, 𝟣𝟧𝘹+𝟤, is the same as the rule of the linear equation 𝘺=𝟣𝟧𝘹+𝟤. 

Write a linear function for the data in each table using linear notation.

Multiple Choice

What is the slope of this linear function?

• $$\frac{1}{5}$$

• 5

• $$-\frac{1}{5}$$

• -5

How to Find Slope

• Find the differences in y-values

• Find the differences in x-values

•  $m\ =\ \frac{\Delta y}{\Delta x}$  

   $m=\frac{5}{1}\ =\ 5$  

Multiple Select

Which is an ordered pair from the table? Select all that apply

• (0,1)

• (1,4)

• (2,9)

• (3,19)

An Ordered Pair

• In a table you can find an ordered pair by looking at the two columns or rows and pairing up the two numbers

• Look in the table and see how when x = 0, y = -1. So the ordered pair is (0,-1)

• The ordered pairs from the table are;

• (0,-1),(1,4),(2,9),(3,14), and (4,19)

Multiple Choice

Which is the correct way to start writing the function using slope-intercept form?

• f(x) = 1/5 x + b

• f(x) = 5x + b

• f(x) = -1/5 x + b

• f(x) = -5x + b

Using slope-intercept form

y = mx + b. Since y is the same thing as f(x), we can say;

f(x) = mx + b

Since we already found the slope to be 5, we just substitute in 5 for m and get;

f(x) = 5x + b

Open Ended

Write the linear function for the data in the table using function notation