Question

Find the slope and y intercept of `sqrt(3x) + (1 - sqrt(3))y` = 3

Answer 1

The equation of a line is `sqrt(3x) + (1 - sqrt(3))y` = 3

`(1 - sqrt(3))y = sqrt(3) x + 3`

y = `(-sqrt(3)x)/(1 - sqrt(3)) + 3/(1 - sqrt(3))`

Slope (m) = `(-sqrt(3))/(1 - sqrt(3))`

= `(-sqrt(3)(1 + sqrt(3)))/((1 - sqrt(3))(1 + sqrt(3))`

= `(-sqrt(3) - 3)/(1 - 3)`

= `(-(sqrt(3) + 3))/(-2)`

= `(sqrt(3) + 3)/2`

y intercept = `3/(1 - sqrt(3))`

= `(3(1 + sqrt(3)))/((1 - sqrt(3))(1 + sqrt(3))`

= `(3 + 3sqrt(3))/(1 - 3)`

= `(3 + 3sqrt(3))/(-2)`

= `-(3(1 + sqrt(3)))/2`