Question

Write an equation in slope-intercept form

Answer 1

Hint :-

• The product of slopes of two perpendicular lines is -1 .
• The slope intercept form of the line is $y = mx + c$ .
• The point slope form of the line is $m(x-x_1) = (y-y_1)$

Solution :-

The given equation to us is ,

$\implies x = \dfrac{-3}{4}y - 5$

Convert it to slope intercept form we have ,

$\implies 4x =-3y -20 \\\\\implies 3y = -4x -20 \\\\\implies y =\dfrac{-4}{3}x -\dfrac{20}{3}$

On comparing to the slope intercept form of the line we have ,

• $m = \dfrac{-4}{3}$

As we know that the product of slopes of two perpendicular lines is-1 , henceforth ,

• $m_{perp}= \dfrac{3}{4}$

Now using slope point form rewrite the equation of the perpendicular line ,

$\implies y-y_1 = m(x-x_1) \\\\\implies y -6 = \dfrac{3}{4}(x+12)\\\\\implies 4y -24 = 3x + 36 \\\\\implies 3x -4y +36+24=0\\\\\implies \underline{\boxed{ \gray{3x -4y +60=0}}}$