Question

Write the standard form of the equation of the line passing through the point (1,2) and perpendicular to the line x-5y=10

Answer 1

5x + y = 7

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange x - 5y = 10 into this form

Subtract x from both sides

- 5y = - x + 10 ( divide all terms by - 5 )

y =
`(1)/(5)` x - 2 ← in point- slope form

with m =
`(1)/(5)`

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m\\)` = -
`(1)/((1)/(5) )` = - 5, thus

y = - 5x + c ← is the partial equation of the line

To find c substitute (1, 2) into the partial equation

2 = - 5 + c ⇒ c = 2 + 5 = 7

y = - 5x + 7 ← in slope - intercept form

Add 5x to both sides

5x + y = 7 ← in standard form