Question

What does the relationship in the table look like graphed?

Answer 1

As it is a linear relationship, we can graph the function based on its equation in the form:

`y=mx+b`

where m is the slope and b is the y-intercept.

To calculate the slope we can choose any two points and display them in the following formula:

`m=(y_2-y_1)/(x_2-x_1)`

Choosing for example (2, 1) and (4, 2):

`m=(2-1)/(4-2)`
`m=(1)/(2)`

Therefore, our equation is:

`y=(1)/(2)x+b`

To calculate b we have to choose again a point, for example, (2, 1) and replace it as follows:

`1=(1)/(2)\cdot2+b`
`1=1+b`
`b=1-1=0`

Finally, our equation is:

`y=(1)/(2)x`

We can use this equation to get other coordinates by choosing any value for x and calculating y. Finally, we get the coordinate (x, y), and to get the line we unite all the points in a line.

Answer:

`y=(1)/(2)x`