Question

A linear function is given by the equation y=4x. Using the points x and x+1, show that the y-values increase by 4 between any two points separated by x2−x1=1

Answer 1

`x_2 - x_1 = 1` gives
`y_2 - y_1 = 4`

Explanation:

Given

`y = 4x`

`(x_1,x_2) = (x,x+1)`

Required

Show that the y values increases by 4 for
`x_2 - x_1 = 1`

We have:

`y = 4x`

For
`x_1 = x`

`y_1 = 4x_1`

Substitute
`x_1 = x`

`y_1 = 4x`

For
`x_2 = x + 1`

`y_2 = 4x_2`

Substitute
`x_2 = x + 1`

`y_2 = 4(x+1)`

`y_2 = 4x+4`

So, we have:

`y_2 = 4x+4`

`y_1 = 4x`

Subtract
`y_1` from
`y_2`

`y_2 - y_1 = 4x + 4 - 4x`

Collect like terms

`y_2 - y_1 = 4x - 4x+ 4`

`y_2 - y_1 = 4`

Hence:

`x_2 - x_1 = 1` gives
`y_2 - y_1 = 4`

i.e. an increment of 4