Question

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

box below.
M(0,6) N(6,0)

Answer 1

`y + x - 6 = 0`

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

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

`m = -1`

The equation of the line can then be calculated using

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

`Using \ m = (y - y_1)/(x - x_1)`

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

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

Multiply both sides by x

`-1 * x = (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 = (y - y_2)/(x - x_2)`

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

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

Multiply both sides by x - 6

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