Question

Write an equation relating the variables in each table

time(x) 1 2 4 6
Distance(y) 15 30 60 90

Answer 1

`y=15x`

Explanation:

Let

x ----> the time

y ----> the distance

we have the points

`(1,15),(2,30),(4,60),(6,90)`

Find the slope m

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

take the points

`(1,15),(6,90)`

substitute in the formula

`m=(90-15)/(6-1)`

`m=(75)/(5)`

`m=15`

Find the linear equation in point slope form

`y-y1=m(x-x1)`

we have

`m=15`

`point\ (1,15)`

substitute

`y-15=15(x-1)` ---> equation in point slope form

Convert to slope intercept form

`y-15=15x-15`

`y=15x-15+15`

`y=15x`

Verify for x=2

`y=15(2)=30` ----> is ok in the table

Verify for x=4

`y=15(4)=60` ----> is ok in the table