Question

If its too blury just ask me to read it to you​

Answer 1

Rate of change:
`m = 5`

The initial value is 20

The equation:
`y = 5x + 20`

Explanation:

Given

The attached table

Solving (a): The rate of change (m)

This is calculated as:

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

Where:

`(x_1,y_1) = (2,30)`

`(x_2,y_2) = (3,35)`

So:

`m = (35- 30)/(3- 2)`

`m = (5)/(1)`

`m = 5`

Solving (b): The initial value

Here, we make use of point (0, y) to calculate the initial value:

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

Where

`(x_1,y_1) = (0,y)`

`(x_2,y_2) = (3,35)`

`m = 5`

So:

`5 = (35 - y)/(3 - 0)`

`5 = (35 - y)/(3)`

Multiply both sides by 3

`3 * 5 = (35 - y)/(3)* 3`

`15 = 35 - y`

`y = 35 - 15`

`y = 20`

Solving (c): The equation

This is calculated using:

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

Where:

`(x_1,y_1) = (2,30)`

`m = 5`

So, we have:

`y = 5(x - 2) + 30`

`y = 5x - 10 + 30`

`y = 5x + 20`