Question

Consider the linear function y = 5x + 12 and the linear function represented by the table of values below.

Answer 1

(a) and (f)

Explanation:

Given

`y = 5x + 12`

See attachment for table and options

First, we calculate the slope of the table

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

Using:

`(x_1,y_1) = (2,29)`

`(x_1,y_1) = (4,53)\\`

So, we have:

`m = (53- 29)/(4 - 2)`

`m = (24)/(2)`

`m = 12`

The equation is then calculated using:

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

This gives:

`y = 12*(x -2) + 29`

`y = 12x -24 + 29`

`y = 12x+5`

So, we have:

`y = 5x + 12` --- The given equation

and

`y = 12x+5` --- The equation of the table

An equation is represented as:

`y = mx + b`

Where:

m = slope or rate of change

b = y intercept

So, for the given equation:
`y = 5x + 12`

Rate of change = 5

y intercept = 12

For the table:
`y = 12x+5`

Rate of change = 12

y intercept = 5

In conclusion:

(a)
`y = 12x+5` has the greater rate of change:

and

(f)
`y = 5x + 12` has the greater y intercept