Question

Indicate in standard form the equation of the line passing through the given points, writing the answer in the equation

Answer 1

Answer:

$y + x - 6 = 0$

Step-by-step explanation:

Given

$M(0,6) \ and \ N(6,0)$

Required

Find the equation of the line

First, the slope of the line has to be calculated using the following formula;

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$where\ (x_1,y_1) = (0,6) \ and \ (x_2,y_2) = (6,0)$

So, the equation becomes

$m = \frac{0 - 6}{6 - 0}$

$m = \frac{-6}{6}$

$m = -1$

The equation of the line can then be calculated using

$m = \frac{y - y_1}{x - x_1} \ or \ m = \frac{y - y_2}{x - x_2}$

$Using \ m = \frac{y - y_1}{x - x_1}$

$-1 = \frac{y - 6}{x -0}$

$-1 = \frac{y - 6}{x}$

Multiply both sides by x

$-1 * x = \frac{y - 6}{x} * x$

$-x = y - 6$

Add x to both sides

$x -x = y - 6 + x$

$0 = y - 6 + x$

Reorder

$y + x- 6 = 0$

$Using \ m = \frac{y - y_2}{x - x_2}$

$-1 = \frac{y - 0}{x - 6}$

$-1 = \frac{y}{x - 6}$

Multiply both sides by x - 6

$-1 * (x-6) = \frac{y}{x - 6} * (x-6)$

$-1 * (x-6) = y$

$-x+6 = y$

Add x - 6 to both sided

$x - 6 -x+6 = y +x - 6$

$0 = y + x - 6$

$y + x - 6 = 0$

Hence, the equation of the line is $y + x - 6 = 0$