Question

What is the equation of the line with slope `m= -31/36` that passes through `(-5/6, 13/18)`?

Answer 1

`216y+186x=1`

Explanation:

Slope of a line `(m) = (y_1-y_2)/(x_1-x_2)` ----(1)

Here , `m=-31/36`

`x_1=x`

`x_2=-5/6`

`y_1=y`

`y_2=13/18`

Put these values in equation(1)

`=> -31/36=(y-13/18)/(x-(-5/6))`

`=> -31/36 = ((18y-13)/cancel18^3)/((6x+5)/cancel6`

`=> -31/cancel36^12=(18y-13)/(cancel3(6x+5)`

Cross-multiply

`=> -31(6x+5)=12(18y-13)`

`=> -186x-155=216y-156`

`=> 156-155=216y+186x`

`=> 1=216y+186x`

Answer 2

`color(orange)(186x + 216y = 1`

Explanation:

Given slope and a point on the line, we can write the equation using

`(y - y_1 ) = m (x - x_1)`

where m is the slope and `(x_1, y_1)` the coordinates of the point.

Hence the equation is

`y - (13/18) = -(31/36) * (x + 5/6)`

`y = -(31/36)x - (31/36)*(5/6) + 13 / 18`

`y = [((-31*6 )x - (31*5) + (13 * 12)) / 216]` L C M 216.

`y = [(-186x - 155 + 156) / 216]`

`y = (-186x + 1) / 216`

`216y = -186x + 1`

`186x + 216y = 1`