Question

Part 1 out of 2Use the graph to make a linear model of each function. Describe the meaning of the termsin the models. Then create the linear system, and state what the solution represents.(700,81)(s) sədreyə SurigF(0,25)(0,4)Call time (min)100 200 100 400 500 600 700 800 900(2)8 (1)The y-intercept, b, of f(t) isand the slope, m, of f(t) isSo f(t)-[ +The y-intercept, b, of g(t) isand the slope, m, of g (t) isSo g(t) =+Question 14 of 20Try AnotherNext Question

Answer 1

We must find 2 line equations, a line equation for the red line and another line equation for the blue one.

For the red line, we have 2 points,

`\begin{gathered} (x_1,y_1)=(0,25) \\ (x_2,y_2)=(700,81) \end{gathered}`

by means of these point and the slope formula

`m=(y_2-y_1)/(x_2-x_1)`

we have

`\begin{gathered} m=(81-25)/(700-0) \\ m=(56)/(700) \\ m=0.08 \end{gathered}`

hence, the form for the red line is

`f(t)=0.08t+b`

Now, the y-intercept b can be obtained by susbtituying point (0,25), that is

`\begin{gathered} 25=0.08(0)+b \\ \text{hence,} \\ b=25 \end{gathered}`

and the red line equation is

`f(t)=0.08t+25`

Now, lets continue with the blue line. In this case, their points are (0,4) and (700,81). Hence, the slope is

`\begin{gathered} m=(81-4)/(700-0) \\ m=(77)/(700) \\ m=0.11 \end{gathered}`

and the y-intercept is b=4. Finally, the blue equation is

`g(t)=0.11t+4`