Question

The graph shows the time, m, in minutes and the temperature, t, in degrees Celsius that it took a pot of ice cubes to melt and boil. The degrees per minute is constant.In the options below, select the phrase that represents the equation that represents the grapht=6.25mm= 6.25tm=t+6.25t= m+6.25

Answer 1

`t=6.25m`

Step-by-step explanation

Step 1

as we can see in the graph, the y axis ( dependent variable ) is for the temperature and the x-axis is for the time, so we need a function where the temperature(t) depends on the time( m)

`t=f(m)`

Step 2

find the slope of the line:

when you have 2 points of the line, you can find the slope by using:

`\begin{gathered} slope=\frac{chang\text{e in y }}{\text{change in }x}=(y_2-y_1)/(x_2-x_1) \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}`

then , let

P1(0,0)

P2(8,50)

now, replace.

`\begin{gathered} slope=(y_2-y_1)/(x_2-x_1) \\ \text{slope}=(50-0)/(8-0)=6.25 \\ \text{slope}=6.25 \end{gathered}`

Step 3

finally, get the equation of the line:

use

`y-y_1=slope(x-x_1)`

now, replace.

`\begin{gathered} y-y_1=slope(x-x_1) \\ y-0_{}=6.25(x-0) \\ y=6.25x \end{gathered}`
`t=f(m)\Rightarrow y=6.25x`

so, the answer is

`t=6.25m`

I hope this helps you