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 temperature be $y$ (in $^{\circ}C$). We can 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 from the table, say $(0,75)$ and $(4.5,95.5)$. The slope $m=\frac{95.5 - 75}{4.5-0}=\frac{20.5}{4.5}=\frac{41}{9}$.
The equation of the line using the point - slope form with the point $(0,75)$ is $y-75=\frac{41}{9}(x - 0)$, so $y=\frac{41}{9}x + 75$.

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

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

Answer:

5.5