Question

2c. The graph represents the relationship between the number oftablespoons of sugar in the bowl and the total weight of the bowl. Whichpoint on the graph could represent your answer to the previous question?800700600С500Bweight (grams)400300 A2001005 10 15 20 25 30 35 40 45 50sugar (tablespoons)Your answer2d. About how many tablespoons of sugar are in the bowl when the totalweight is 600 grams?

Answer 1

The solution to b , c and d are 32 , Point D and 20.8 respectively.

To solve , we need to obtain the equation for the regression line, which can be written in the form : y = bx + c

• b = slope ; c = intercept

From the graph;

Slope = Rise / Run

Slope = (740 - 340) / (32 - 0) = 12.5

From the graph, the Intercept is the value of y where the line cross x = 0 ;

• c = y - Intercept = 340

The regression equation becomes : y = 12.5x + 340

2b.)

y = weight ; At y = 740

put y = 740 in the equation and find x :

740 = 12.5x + 340

740 - 340 = 12.5x

400 = 12.5x

x = 400/12.5

x = 32

Hence, 32 tablespoons of sugar would be needed.

c.)

The point on the graph which could represent 32 teaspoonful is D.

d.)

Number of tablespoons of sugar when bowl weighs 600 grams

put y = 600

600 = 12.5x + 340

600 - 340 = 12.5x

260 = 12.5x

x = 260/12.5

x = 20.8

Answer 2

Final answer for 2c

`\begin{gathered} \text{when the bowl has zero table spoons of sugar,} \\ y=mx+c \\ c=350 \\ m=\text{ }(520-350)/(15-0) \\ m=1.485 \\ y=\text{ 11.33x + 350} \\ \text{where y is total weight} \\ \text{and x is table spoons of sugar} \\ \end{gathered}`

Final answer for 2d

Point D answers the question in 2b

`\begin{gathered} y=\text{ 1.485x + 350} \\ y=\text{ 600g} \\ 600\text{ = 11.33x + 350} \\ x=\text{ }(600-350)/(11.33) \\ x=22\text{ tablespoons} \end{gathered}`