Question

Write an equation of a line that is perpendicular to the line 2x-3y+15=0

Answer 1

Answer:

$y =- \frac{3}{2} x+1$

Step-by-step explanation:

The equation of the given straight line is 2x - 3y + 15 = 0.

Now, we can express the equation as 3y = 2x + 15

⇒ $y = \frac{2}{3} x+ 5$ ..........(1)

The equation is in slope-intercept form and the slope is =$\frac{2}{3}$

Therefore, the equation of a straight line which is perpendicular to (1) is  

$y = -\frac{3}{2} x+c$ {Where c is any constant}

{Since, the product of slopes of two perpendicular straight lines is -1}

Now, putting c = 1, we get the equation as $y =- \frac{3}{2} x+1$. (Answer)