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?
5
5.5
6
6.5

Explanation:

Step1: Assume linear - relationship

Let the time be $x$ (in minutes) and the temperature be $y$ (in $^{\circ}C$). We use the two - point form of a line $y - y_1=\frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$. Let's take two points $(0,75)$ and $(4.5,95.5)$.

Step2: Calculate the slope

The slope $m=\frac{95.5 - 75}{4.5-0}=\frac{20.5}{4.5}=\frac{41}{9}\approx4.56$.

Step3: Find the equation of the line

Using the point - slope form with the point $(0,75)$, the equation of the line is $y-75=\frac{41}{9}(x - 0)$, so $y=\frac{41}{9}x + 75$.

Step4: Solve for $x$ when $y = 100$

Set $y = 100$, then $100=\frac{41}{9}x+75$. 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