Adirect variation function contains the points (–8, –6) and (12, 9). which equation represents the function?

a. y = –4/3x
b. y = –3/4x
c. y = 3/4x
d. y = 4/3x

Option C.

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form or

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

so

Find the value of the constant k

For the point (-8,-6)

For the point (12,9)

Note A single point was required to find the constant k (because the line passes through the origin)

The equation is equal to

i think it is 18

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is