Question

A swimmer is practicing for team tryouts andrecords the number of laps she swims and theamount of time it takes on four separate daysThe table represents the number of laps and thetime taken to swim the laps on each of thosedaysTime (in seconds)Number of Laps4121520144240340The swimmer wants to estimate the amount oftime it will take to swim 10 laps. If x representsthe number of laps, and y represents the time, inseconds, which statement is true?

Answer 1

The form of the linear equation is y = m x + b

m is the slope of the line, the rule of m is

$m=\frac{y2-y1}{x2-x1}$

b is the y-intercept, value y at x = 0

Let us use two points from the table to find m

(4, 96) and (12, 144)

x1 = 4 and y1 = 96

x2 = 12 and y2 = 144

Substitute them in the rule of the slope to find it

$m=\frac{144-96}{12-4}=6$

(12, 144) and (15, 240)

x1 = 12 and y1 = 144

x2 = 15 and y2 = 240

$m=\frac{240-144}{15-12}=32$

(15, 240) and (20, 340)

x1 = 15 and y1 = 240

x2=20 and y2 = 340

$m=\frac{340-240}{20-15}=20$

We need to find the best estimate of the slope from these 3 numbers

We will choose m = 15.3

Then the equation will be one of A or B let us check the time for x = 10

y = 15.3(10) + 10.4 = 163.4

Then the answer is A