Question

write the equation of a line that is perpendicular to the line y=-3/4x+3 and passes through the point (3,7). Write your answer in BOTH point-slope form and 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 )

y = -
`(3)/(4)` x + 3 ← is in slope- intercept form

with slope m = -
`(3)/(4)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(3)/(4) )` =
`(4)/(3)` , then

y =
`(4)/(3)` x + c ← is the partial equation

To find c substitute (3, 7 ) into the partial equation

7 = 4 + c ⇒ c = 7 - 4 = 3

y =
`(4)/(3)` x + 3 ← in slope- intercept form

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Here m =
`(4)/(3)` and (a, b ) = (3, 7 ) , then

y - 7 =
`(4)/(3)` (x - 3) ← in point- slope form