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

$t=6.25m$

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:

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

then , let

P1(0,0)

P2(8,50)

now, replace.

$\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{50-0}{8-0}=6.25 \\ \text{slope}=6.25 \end{gathered}$

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