Answer:
[tex]y = x + 6[/tex]
Step-by-step 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
[tex](x_1,y_1)(x_2,y_2) = (0,6)(-6,0)[/tex]
Next is to determine the slope of the line using the following formula
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Substitute [tex](x_1,y_1)(x_2,y_2) = (0,6)(-6,0)[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes
[tex]m = \frac{0 - 6}{-6 - 0}[/tex]
[tex]m = \frac{- 6}{-6}[/tex]
[tex]m = 1[/tex]
Next is to determine the equation using slope formula
[tex]m = \frac{y - y_1}{x - x_1}\ or\ m = \frac{y - y_2}{x - x_2}[/tex]
using
[tex]m = \frac{y - y_1}{x - x_1}\ where\ m = 1\ x_1 = 0\ and \ y_1 = 6[/tex]
[tex]1 = \frac{y - 6}{x - 0}[/tex]
[tex]1 = \frac{y-6}{x}[/tex]
Multiply both sides by x
[tex]x * 1 = x * \frac{y-6}{x}[/tex]
[tex]x = y - 6[/tex]
Add 6 to both sides
[tex]x + 6 = y - 6 + 6[/tex]
[tex]x + 6 = y[/tex]
[tex]y = x + 6[/tex]
Hence, the equation of the line is [tex]y = x + 6[/tex]
