Question

Determine whether y varies directly with x. If so,

Find the constant of variation k, and
Write the equation

x, 8 10, 12, 14
y, 12, 15, 18, 21
(in that order)

Answer 1

Answer is yes, y varies directly with x.
Each x increases by 2 and each y increases by 3.
the rate is proportional, each y/x set = 3/2 rate or slope
Equation is y= 3/2x

Step by step

To check if the set is proportional, divide y/x for each set of points. Here each one equals 3/2, so they are proportional.

Next it says to find the constant of variation k, which we already did by y/x slope is 3/2.

Next to find the equation.
We will use our slope 3/2 and points (8, 12) and plug these into formula

(Y - y1) = m (x - x1)

Y - 12 = 3/2 (x - 8)

Distribute

Y - 12 = 3/2x - 12

Add 12 to both sides to isolate y

y = -12 + 12 = 3/2x -12 + 12

Combine

y = 3/2x