Find the equation of a line which is perpendicular to the line joining (4,2) and (3,5) and cuts off and intercept of length 3 on y-axis.

Explanation

Slope `m =frac(y_2-y_1)(x_2-x_1)=frac(5-2)(3-1)=-3`

Slope of a line perpendicular to the line `(y=m x+c)` is `frac(-1)m` with y-intercept 3 units.

therefore Slope of a line perpendicular to the line` y=m x+c ` is ` frac(-1)(-3)`=`frac(1)(3)` with y-intercept 3 units.

Thus, the required equation is `y=(frac(1)3) x+3` or `3 y=x+9 `or `x-3 y+9=0`