Question

(15, 2); perpendicular to 5x - y = 2

(a) Write the equation of the line in slope-intercept form.
(b) Write the equation of the line in standard form.

Answer 1

see explanation

Explanation:

the equation of a line in slope- intercept form is

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

given

5x - y = 2 ( subtract 5x from both sides )

- y = - 5x + 2 ( multiply through by - 1 )

y = 5x - 2 ← in slope- intercept form

with slope m = 5

(a)

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

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

y = -
`(1)/(5)` x + c ← is the partial equation

to find c substitute (15, 2 ) into the partial equation

2 = -
`(1)/(5)` (15) + c = - 3 + c ( add 3 to both sides )

5 = c

y = -
`(1)/(5)` x + 5 ← in slope- intercept form

(b)

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

y = -
`(1)/(5)` x + 5 ( multiply through by 5 to clear the fraction )

5y = - x + 25 ( add x to both sides )

x + 5y = 25 ← in standard form