Question

linear functions part 2

1. noah placed an empty bowl on a scale. he added different amounts of a liquid to the bowl, recording the amount of liquid added, in tablespoons, and the total weight of the bowl and liquid, in grams. each time on a scatter - plot. he fit the line y = 14.75x+88.182 to the data in his scatter - plot, where x represents the amount of the liquid, in tablespoons, and y represents the total weight of the bowl and the liquid, in grams.

a. interpret the slope of the line based on the context.
b. interpret the y - intercept of the line based on the context.
c. determine the weight, in grams, when 11 tablespoons of the liquid are placed in the bowl.
weight (grams)
d. determine the approximate number of tablespoons of the liquid noah needs to add so that the total weight is 1,200 grams.
amount of liquid (tablespoons)

Explanation:

Step1: Identify linear - equation form

The equation is $y = 14.75x+88.182$, where $x$ is amount of liquid and $y$ is total weight.

Step2: Interpret slope

The slope 14.75 means each tablespoon of liquid adds 14.75 grams.

Step3: Interpret y - intercept

The y - intercept 88.182 is the weight of the empty bowl.

Step4: Find weight for 11 tablespoons

Substitute $x = 11$ into $y=14.75\times11 + 88.182=240.432$ grams.

Step5: Find amount for 1200 grams

Set $y = 1200$ and solve for $x$: $1200=14.75x + 88.182$, $x=\frac{1200 - 88.182}{14.75}\approx75.49\approx75$ tablespoons.

Answer:

a. Each tablespoon of liquid adds 14.75 grams.
b. Weight of empty bowl is 88.182 grams.
c. 240.432 grams
d. 75 tablespoons