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

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

Explanation:

Step1: Assume linear - relationship

Let the linear equation be $y = mx + b$, where $y$ is the temperature ($\text{T}$) and $x$ is the time ($t$). We can use two - point form to find the equation of the line. Let's take two points $(t_1,y_1)=(0,75)$ and $(t_2,y_2)=(0.5,79)$.
The slope $m=\frac{y_2 - y_1}{t_2 - t_1}=\frac{79 - 75}{0.5-0}=\frac{4}{0.5}=8$.
Using the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(0,75)$, the equation of the line is $y=8t + 75$.

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

Set $y = 100$ in the equation $y=8t + 75$.
We get $100=8t + 75$.
Subtract 75 from both sides: $100 - 75=8t$, so $25 = 8t$.
Then $t=\frac{25}{8}=3.125$ minutes.

Answer:

$3.125$ minutes