Question

a direct variation function contains the points (-8 -6) and (12,9) which equation represents the function?


1: Y=-4/3x

2: Y=-3/4x

3: Y=3/4x

4:y=4/3x​

Answer 1

Answer

Option C. y=(3/4)xy=(3/4)x

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 y/x=ky/x=k or y=kxy=kx

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)

k=y/x=(-6/-8)=3/4k=y/x=(−6/−8)=3/4

For the point (12,9)

k=y/x=(9/12)=3/4k=y/x=(9/12)=3/4

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

The equation is equal to

y=(3/4)xy=(3/4)x

Answer 2

The answer is... Step-by-step explanation: y = 1/3x --or-- y = x/3 Both forms of writing are equivalent, so either choice would be correct. I hope this helps! 

Step-by-step explanation:

Answer: Step-by-step explanation: First, find the rate of change [slope]: Then plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula since you get it done much swiftly that way. It does not matter which ordered pair you choose: −4 = ⅓[−12] + b −4 _______________________________________________ −3 = ⅓[−9] + b −3