The word is divides the sentence into what should be on the left-hand side and what should be on the right-hand side of the equation.
Function Rule: y=1/3x Graph:
Practice makes perfect
We have been given a sentence and we need to translate it into an equation.
The output is one-third of the input.
Every equation has an equals sign and values or expressions on either side of it. Key phrases, such as is,is equal to, and equals tell us about the placement of the equals sign.
The output is one-third of the input.
⇕
The output = one-third of the input.
On the left-hand side, we only have the key word output, which we will name as the variable y.
The output = one-third of the input.
⇕
y = one-third of the input.
On the right-hand side, the key word is input. This word represents the variable x.
one-third of the input.
⇕
1/3 x
Putting these sides together, we have a complete equation.
y = 1/3 x
Let's now graph the function. To graph the function y= 13x, we will follow two steps.
Graph the ordered pairs and draw the line through them.
Let's do these things one at a time.
Making a Function Table
To make a function table, we will select some values of x which will be part of our domain. Then, we will substitute these values in the function to find the corresponding values of y. These x- and y-values will create a set of ordered pairs.
x
1/3x
y
(x,y)
0
1/3( 0)
0
( 0, 0)
3
1/3( 3)
1
( 3, 1)
6
1/3( 6)
2
( 6, 2)
9
1/3( 9)
3
( 9, 3)
We found four ordered pairs that lie on the graph of our function.
Graphing the Ordered Pairs and Drawing the Line
Next, we will graph the ordered pairs and connect them with a straight line.
The line is the complete graph of the function. The ordered pairs corresponding to any points on the line are solutions of the equation y= 13x.
