Question

A recipe for chocolate chip cookies uses 3 tablespoons of cookie batter for every 2 tablespoons of chocolate chips. The line represents the relationship between the amount of cookie batter and the amount of chocolate chips needed to make a batch of cookies according to the recipe. The point (1, 1.5) is on the line. Label the axes appropriately. (1.1.5)

Answer 1

EXPLANATION

Let's see the facts:

Recipe:

3 tablespoons of cookies ------> 2 tablespoons of chocolate chips

Let x be the tablespoons of chocolate chips and y be the tablespoons of cookies.

The point (1,1.5) is a part of the line, so x=1 and y=1.5

So, we have two ordered pairs:

(x_1,y_1)= (1,1.5) and (x_2,y_2)= (2,3)

The slope is given by the following equation:

`\text{Slope}=(y_2-y_1)/(x_2-x_1)=(3-1.5)/(2-1)=(1.5)/(1)=1.5=3/2`

The line equation is:

y = (3/2)x + b where m= 3/2 and b is the y-intercept

Now, subtituting either one ordered pair:

3=(3/2)*(2) + b

Multiplying terms:

3 = 3 + b

Subtracting -3 to both sides:

3 - 3 = b

Simplifying:

0 = b

Switching sides: b = 0

So the equation is:

y = (3/2)x

Now, mapping the line: