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Answer :
Certainly! Let's walk through how to create a chart of inputs and outputs for the function [tex]\( y = \frac{2}{5} x \)[/tex] and then write the ordered pairs, starting with an input of 0 and ending with 10.
1. Determine the Inputs:
We'll use the inputs [tex]\( x = 0, 1, 2, \ldots, 10 \)[/tex]. These are just the numbers from 0 to 10.
2. Calculate the Outputs:
For each input [tex]\( x \)[/tex], calculate the output using the formula [tex]\( y = \frac{2}{5} x \)[/tex].
- For [tex]\( x = 0 \)[/tex]: [tex]\( y = \frac{2}{5} \times 0 = 0 \)[/tex]
- For [tex]\( x = 1 \)[/tex]: [tex]\( y = \frac{2}{5} \times 1 = \frac{2}{5} \)[/tex]
- For [tex]\( x = 2 \)[/tex]: [tex]\( y = \frac{2}{5} \times 2 = \frac{4}{5} \)[/tex]
- For [tex]\( x = 3 \)[/tex]: [tex]\( y = \frac{2}{5} \times 3 = \frac{6}{5} \)[/tex]
- For [tex]\( x = 4 \)[/tex]: [tex]\( y = \frac{2}{5} \times 4 = \frac{8}{5} \)[/tex]
- For [tex]\( x = 5 \)[/tex]: [tex]\( y = \frac{2}{5} \times 5 = 2 \)[/tex]
- For [tex]\( x = 6 \)[/tex]: [tex]\( y = \frac{2}{5} \times 6 = \frac{12}{5} \)[/tex]
- For [tex]\( x = 7 \)[/tex]: [tex]\( y = \frac{2}{5} \times 7 = \frac{14}{5} \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( y = \frac{2}{5} \times 8 = \frac{16}{5} \)[/tex]
- For [tex]\( x = 9 \)[/tex]: [tex]\( y = \frac{2}{5} \times 9 = \frac{18}{5} \)[/tex]
- For [tex]\( x = 10 \)[/tex]: [tex]\( y = \frac{2}{5} \times 10 = 4 \)[/tex]
3. Write the Ordered Pairs:
For each input, pair it with its corresponding output, creating ordered pairs [tex]\((x, y)\)[/tex].
- [tex]\((0, 0)\)[/tex]
- [tex]\((1, \frac{2}{5})\)[/tex]
- [tex]\((2, \frac{4}{5})\)[/tex]
- [tex]\((3, \frac{6}{5})\)[/tex]
- [tex]\((4, \frac{8}{5})\)[/tex]
- [tex]\((5, 2)\)[/tex]
- [tex]\((6, \frac{12}{5})\)[/tex]
- [tex]\((7, \frac{14}{5})\)[/tex]
- [tex]\((8, \frac{16}{5})\)[/tex]
- [tex]\((9, \frac{18}{5})\)[/tex]
- [tex]\((10, 4)\)[/tex]
Now, we have our chart with ordered pairs from inputs 0 through 10. Each pair represents a point on the line defined by the equation [tex]\( y = \frac{2}{5} x \)[/tex].
1. Determine the Inputs:
We'll use the inputs [tex]\( x = 0, 1, 2, \ldots, 10 \)[/tex]. These are just the numbers from 0 to 10.
2. Calculate the Outputs:
For each input [tex]\( x \)[/tex], calculate the output using the formula [tex]\( y = \frac{2}{5} x \)[/tex].
- For [tex]\( x = 0 \)[/tex]: [tex]\( y = \frac{2}{5} \times 0 = 0 \)[/tex]
- For [tex]\( x = 1 \)[/tex]: [tex]\( y = \frac{2}{5} \times 1 = \frac{2}{5} \)[/tex]
- For [tex]\( x = 2 \)[/tex]: [tex]\( y = \frac{2}{5} \times 2 = \frac{4}{5} \)[/tex]
- For [tex]\( x = 3 \)[/tex]: [tex]\( y = \frac{2}{5} \times 3 = \frac{6}{5} \)[/tex]
- For [tex]\( x = 4 \)[/tex]: [tex]\( y = \frac{2}{5} \times 4 = \frac{8}{5} \)[/tex]
- For [tex]\( x = 5 \)[/tex]: [tex]\( y = \frac{2}{5} \times 5 = 2 \)[/tex]
- For [tex]\( x = 6 \)[/tex]: [tex]\( y = \frac{2}{5} \times 6 = \frac{12}{5} \)[/tex]
- For [tex]\( x = 7 \)[/tex]: [tex]\( y = \frac{2}{5} \times 7 = \frac{14}{5} \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( y = \frac{2}{5} \times 8 = \frac{16}{5} \)[/tex]
- For [tex]\( x = 9 \)[/tex]: [tex]\( y = \frac{2}{5} \times 9 = \frac{18}{5} \)[/tex]
- For [tex]\( x = 10 \)[/tex]: [tex]\( y = \frac{2}{5} \times 10 = 4 \)[/tex]
3. Write the Ordered Pairs:
For each input, pair it with its corresponding output, creating ordered pairs [tex]\((x, y)\)[/tex].
- [tex]\((0, 0)\)[/tex]
- [tex]\((1, \frac{2}{5})\)[/tex]
- [tex]\((2, \frac{4}{5})\)[/tex]
- [tex]\((3, \frac{6}{5})\)[/tex]
- [tex]\((4, \frac{8}{5})\)[/tex]
- [tex]\((5, 2)\)[/tex]
- [tex]\((6, \frac{12}{5})\)[/tex]
- [tex]\((7, \frac{14}{5})\)[/tex]
- [tex]\((8, \frac{16}{5})\)[/tex]
- [tex]\((9, \frac{18}{5})\)[/tex]
- [tex]\((10, 4)\)[/tex]
Now, we have our chart with ordered pairs from inputs 0 through 10. Each pair represents a point on the line defined by the equation [tex]\( y = \frac{2}{5} x \)[/tex].
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