Question

the table shows the temperature of an amount of water set on a stove to boil, recorded every half minute. waiting for water to boil

time (min)	0	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4	4.5
temp. (°c)	75	79	83	86	89	91	93	94	95	95.5

according to the line of best fit, at what time will the temperature reach 100°c, the boiling point of water?
o 5
o 5.5
o 6
o 6.5

Explanation:

Step1: Assume linear - regression model

Let the time be $x$ (in minutes) and the temperature be $y$ (in °C). The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
We can use two - point form to estimate the equation of the line. Let's take two points $(x_1,y_1)=(0,75)$ and $(x_2,y_2)=(4.5,95.5)$.
The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{95.5 - 75}{4.5-0}=\frac{20.5}{4.5}=\frac{41}{9}\approx4.56$.
Using the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(0,75)$, we get $y=mx + 75=\frac{41}{9}x+75$.

Step2: Solve for $x$ when $y = 100$

Set $y = 100$ in the equation $y=\frac{41}{9}x+75$.
$100=\frac{41}{9}x+75$.
Subtract 75 from both sides: $100 - 75=\frac{41}{9}x$, so $25=\frac{41}{9}x$.
Then $x=\frac{25\times9}{41}=\frac{225}{41}\approx5.5$.

Answer:

5.5