Question

Please help! 2 math problems about slope intercept 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 )

(1)

Given

y - 3 = - 2(x + 5) ← distribute parenthesis

y - 3 = - 2x - 10 ( add 3 to both sides )

y = - 2x - 7 ← in slope- intercept form

(2)

y = 3x + 5 ← is in slope- intercept form

with slope m = 3

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

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

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

To find c substitute (3, - 2) into the partial equation

- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1

y = -
`(1)/(3)` x - 1 ← equation of line