Question

1

Write an equation for the linear
relationship shown below.
4
1
6
7
8
13
10
19

Answer 1

`\bold{y=3x-11}`

Explanation:

Begin with the equation
`y=mx+b`. Let's first find
`m`.

For each time
`x` increases by 2 (the rows skip by 2),
`y` increases by 6. Since the relationship is linear, if
`x` were to increase by just 1 (half of 2),
`y` would increase by 3 (since we halve each component). Therefore,
`m=3`.

To find
`b` (the y-intercept), we plug in the first value of
`x` we are given and notice the result. In this case,
`4 *3=12`. However, the first value of
`y` is 1, so we must subtract 11 so that the first term is 1. Hence,
`y=3x+11`.