Question

Determine the equation of a line passing through `(sqrt2, 2sqrt2) "with slope"  2/3`.

Answer 1

Given values:

Point `(x_1, y_1) = (sqrt2, 2sqrt2)`

Slope (m) = `2/3`

Using the point–slope formula:

y − y₁ = m(x − x₁)

`y - 2sqrt2 = 2/3 (x-sqrt2)`

`3(y - 2sqrt2) = 2(x - sqrt2)`     ...[Multiplied both sides by 3 to eliminate the fraction]

`3y - 6sqrt2 = 2x - 2sqrt2`

0 = `2x - 3y - 2sqrt2 + 6sqrt2`

∴ `2x - 3y + 4sqrt2 = 0`

Hence, the equation of the line is `2x - 3y + 4sqrt2 = 0`