Question

Enter and equation relating the variables in the table. Express any value(s) in your answer as simplified fractions, if necessary.

Time (x) - 18, 45, 72, 81

Distance (y) - 8, 20, 32, 36

The equation is y =

Answer 1

`y=\frac49x`

Explanation:

Let
`(x_1,y_1)` = (45, 20)

Let
`(x_2,y_2)` = (72, 32)

using slope formula to find slope
`m`:

`m=(y_2-y_1)/(x_2-x_1)=(32-20)/(72-45)=\frac49`

using point-slope formula:

`y-y_1=m(x-x_1)`

`\implies y-20=\frac49(x-45)`

`\implies y-20=\frac49x-20`

`\implies y=\frac49x`