Clare has a recipe for yellow cake. She uses 9 ⅓ cups of flour to make 4 cakes. Noah will follow the same recipe. He will make c cakes using f cups of flour. Which of these equations represent the relationship between cake and flour?

Relationship between c and f is 7c - 3f = 0

Step-by-step explanation:

Since Clare has to use 9 cups each of them having 1/3 part filled with flour for making of 4 cakes.

Implies that 4 cakes require 28/3 cups of flour.

So 1 cake will require 28/4 x 3 cups of flour.

And c cakes will require 28c/12 cups of flour.

Hence according to the question

28c/12 = f

⇒ 28c = 12f

⇒ 7c = 3f

⇒ 7c - 3f = 0 is required equation.

y = 2x - 5

the equation of a line in slope- intercept form is

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

rearrange 2x - y = 6 into this form ( subtract 2x from both sides )

- y = - 2x + 6 ( multiply through by - 1 )

y = 2x - 6 ← in slope -intercept form with slope m = 2

Parallel lines have equal slopes

the partial equation is y = 2x + c

to find c substitute (2, - 1 ) into the partial equation

- 1 = 4 + c ⇒ c = - 1 - 4 = - 5

y = 2x - 5 ← equation of parallel line