Write the equation of a line that is perpendicular to the given line and that passes through the given point. y= 2/3x + 9 ; (–6, 5)

y = - x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

y = x + 9 ← is in slope- intercept form

with slope m =

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

= - = - = - , thus

y = - x + c ← is the partial equation

To find c substitute (- 6, 5) into the partial equation

5 = 9 + c ⇒ c = 5 - 9 = - 4

y = - x - 4 ← equation of perpendicular line

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.