Question

Find the equation of the line that passes through the point (2, 1) and is perpendicular to y=(−2/5)x+3.

Answer 1

Explanation:

perp. 5/2

y - 1 = 5/2(x - 2)

y - 1 = 5/2x - 5

y = 5/2x - 4

Answer 2

The answer is

`y = (5)/(2) x - 4`

Explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the perpendicular line we must first find the slope of the original line

The original line is y = - 2/5x + 3

Comparing with the general equation above

Slope/m = - 2/5

Since the lines are perpendicular to each other the slope of the perpendicular line is the negative inverse of the original line

So we have

`m * m _1 = - 1 \\ - (2)/(5) m _1 = - 1 \\ = - 2m _1 = - 5 \\ = m _1 = (5)/(2)`

So the slope of the perpendicular line is

5/2

So the equation of the line using point

(2, 1) and slope 5/2 is

`y - 1 = (5)/(2) (x - 2) \\ y - 1 = (5)/(2) x - 5 \\ y = (5)/(2) x - 5 + 1`

We have the final answer as

`y = (5)/(2) x - 4`

Hope this helps you