Question

PLEASE HELP

This table models a linear function.

x -8 -4 4 8
y -1 0 2 3

Enter the coordinates of the y-intercept in the boxes.

Answer 1

`(x,y) = (0,1)`

Explanation:

Given

The above table

Required

Determine the coordinates of the y intercept

Represent points on the table as:

`(x_1,y_1) = (4,2)`

`(x_2,y_2) = (8,3)`

First, calculate slope (m):

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

`m = (3-2)/(8 - 4)`

`m = (1)/(4)`

For y intercept, the following coordinate point exist:

`(x_3,y_3) = (0,y)`

Because x = 0 at y intercept

Calculate the slope as:

`m = (y_3 - y_1)/(x_3 - x_1)`

The equation becomes

`(1)/(4) = (y - 2)/(0 - 4)`

`(1)/(4) = (y - 2)/(- 4)`

Cross Multiply:

`4(y-2) = -4 * 1`

Divide through by 4

`y - 2 = -1 * 1`

`y - 2 = -1`

Make y the subject:

`y = 2-1`

`y = 1`

Hence, the coordinates of the y intercept is:

`(x,y) = (0,1)`