Question

Write an equation that represents the line (use exact numbers)

(please help me, I've been stuck on this question for a while :/)

Answer 1

`y = x + 6`

Explanation:

Given

The attached graph

Required

Find the equation of the graph

First, we have to get the coordinates of any two points on the graph;

Point 1:

When x = 0; y = 6

Point 2:

When x = -6, y = 0

So, at this stage;we have two coordinates

`(x_1,y_1)(x_2,y_2) = (0,6)(-6,0)`

Next is to determine the slope of the line using the following formula

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

Substitute
`(x_1,y_1)(x_2,y_2) = (0,6)(-6,0)`

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

`m = (0 - 6)/(-6 - 0)`

`m = (- 6)/(-6)`

`m = 1`

Next is to determine the equation using slope formula

`m = (y - y_1)/(x - x_1)\ or\ m = (y - y_2)/(x - x_2)`

using

`m = (y - y_1)/(x - x_1)\ where\ m = 1\ x_1 = 0\ and \ y_1 = 6`

`1 = (y - 6)/(x - 0)`

`1 = (y-6)/(x)`

Multiply both sides by x

`x * 1 = x * (y-6)/(x)`

`x = y - 6`

Add 6 to both sides

`x + 6 = y - 6 + 6`

`x + 6 = y`

`y = x + 6`

Hence, the equation of the line is
`y = x + 6`