Question

PLEASE HELP ASAP

A line that passes through the points (-1, -4) and (4, 2) is shown.
Which equation is the equation of the line that is perpendicular to the given line and passes through the point (-3, 7) ?

Answer 1

D

Explanation:

slope of the given line :

(-4-2)/(-1-4)

-6/-5

6/5

slope of a perpendicular line : -5/6

y-7 = -5/6 (x-(-3)

y -7 = -5/6 (x+3)

y -7 = -5/6 x - 5/2

5/6 x + y - 7 + 5/2 = 0

5/6 x + y + (-14 + 5)/2 = 0

5/6 x + y - 9/2 = 0

5x + 6y - 27= 0

5x + 6y = 27

Answer 2

D

Explanation:

the equation of a line in slope- intercept form is

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

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 1, - 4 ) and (x₂, y₂ ) = (4, 2 )

m =
`(2-(-4))/(4-(-1))` =
`(2+4)/(4+1)` =
`(6)/(5)` ← slope of graphed line

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

`m_{perpendicular` = -
`(1)/(m)` = -
`(1)/((6)/(5) )` = -
`(5)/(6)` , then

y = -
`(5)/(6)` x + c ← is the partial equation of the perpendicular line

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

7 =
`(5)/(2)` + c ⇒ c = 7 -
`(5)/(2)` =
`(14)/(2)` -
`(5)/(2)` =
`(9)/(2)`

y = -
`(5)/(6)` x +
`(9)/(2)` ← equation in slope- intercept form

multiply through by 6 ( the LCM of 6 and 2 ) to clear the fractions

6y = - 5x + 27 ( add 5x to both sides )

5x + 6y = 27 ← equation of perpendicular line in standard form