Question

Write the equation of the line that passes through (–2, 1) and is perpendicular to the line 3x – 2y = 5.

Answer 1

y =
`-(2)/(3) x` -
`(1)/(3)`

Explanation:

The line (l1) passes through (-2, 1) and is perpendicular to the line whose equation is;

3x - 2y = 5

Converting this equation to slope intercept form gives;

2y = 3x - 5

y = 1.5x - 2.5

Let the slope of the perpendicular line (l2) be m(PERP).

The product of slopes of two perpendicular lines is -1

The slope of our first line (l1) = 1.5

So 1.5 × m(PERP) = -1

m(PERP) = -1 ÷ 1.5 =
`-(2)/(3)`

Taking another point (x,y) on line (l2);

`(y - 1)/(x + 2) = -(2)/(3)`

Cross multiplying this gives;

y =
`-(2)/(3) x` -
`(1)/(3)`

which is the equation of our second line (l2).