Question

Write an equation that is perpendicular to
3x - 5y = 5 and passes through the point
(9, -14).

Answer 1

Answer:

$y=-\frac{5}{3}x+1$

Step-by-step explanation:

Given:

Equation of the line.

$3x-5y=5$

And passes through the point (9, -14)

Solution:

Now, we have to write an equation that is perpendicular to 3x -5y = 5 and passes through the point (9, -14).

Now, we write the given equation in $y=mx+b$ form.

$3x-5y=5$

$5y=3x-5$

$y=\frac{3}{5}x-\frac{5}{5}$

$y=\frac{3}{5}x-1$

So, the slope of the line is $m=\frac{3}{5}$.

The slope of the perpendicular line is $-\frac{1}{m}$

now, we substitute m value in above relation.

$=-\frac{1}{\frac{3}{5}}$

$=-\frac{5}{3}$

So the equation of the perpendicular line is:

$y=-\frac{5}{3}x+b$--------(1)

Lets us find  b from the given points (9, -14).

$-14=-\frac{5}{3}\times 9+b$

$-14=-5\times 3+b$

$-14=-15+b$

$b=15-14$

$b=1$

Now, we substitute b value in equation 1.

$y=-\frac{5}{3}x+1$

Therefore, the equation of the perpendicular line is

$y=-\frac{5}{3}x+1$