Answer:
[tex]y + x - 6 = 0[/tex]
Step-by-step explanation:
Given
[tex]M(0,6) \ and \ N(6,0)[/tex]
Required
Find the equation of the line
First, the slope of the line has to be calculated using the following formula;
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]where\ (x_1,y_1) = (0,6) \ and \ (x_2,y_2) = (6,0)[/tex]
So, the equation becomes
[tex]m = \frac{0 - 6}{6 - 0}[/tex]
[tex]m = \frac{-6}{6}[/tex]
[tex]m = -1[/tex]
The equation of the line can then be calculated using
[tex]m = \frac{y - y_1}{x - x_1} \ or \ m = \frac{y - y_2}{x - x_2}[/tex]
[tex]Using \ m = \frac{y - y_1}{x - x_1}[/tex]
[tex]-1 = \frac{y - 6}{x -0}[/tex]
[tex]-1 = \frac{y - 6}{x}[/tex]
Multiply both sides by x
[tex]-1 * x = \frac{y - 6}{x} * x[/tex]
[tex]-x = y - 6[/tex]
Add x to both sides
[tex]x -x = y - 6 + x[/tex]
[tex]0 = y - 6 + x[/tex]
Reorder
[tex]y + x- 6 = 0[/tex]
[tex]Using \ m = \frac{y - y_2}{x - x_2}[/tex]
[tex]-1 = \frac{y - 0}{x - 6}[/tex]
[tex]-1 = \frac{y}{x - 6}[/tex]
Multiply both sides by x - 6
[tex]-1 * (x-6) = \frac{y}{x - 6} * (x-6)[/tex]
[tex]-1 * (x-6) = y[/tex]
[tex]-x+6 = y[/tex]
Add x - 6 to both sided
[tex]x - 6 -x+6 = y +x - 6[/tex]
[tex]0 = y + x - 6[/tex]
[tex]y + x - 6 = 0[/tex]
Hence, the equation of the line is [tex]y + x - 6 = 0[/tex]
