Question

Hello I would like help with both of these questions

Answer 1

Solution

- The slope of a linear equation is given by:

$\begin{gathered} Given \\ y=mx+c \\ \\ m=slope\text{ of the equation} \end{gathered}$

- We can compare this general equation to the first equation given to us as follows:

$\begin{gathered} f(x)=2x+3 \\ y=mx+c \\ \\ \therefore m=2,c=3 \end{gathered}$

- Thus, the slope of the first equation is 2

- The second equation can be gotten by following the logic of the production of the filters and then generalize.

- That is,

$\begin{gathered} \text{ Hour = 1} \\ \text{ Number of filters}=400 \\ \\ \text{ Hour }=2 \\ \text{ Number of filters }=400\times2=800 \\ \\ \text{ Hour}=3 \\ \text{ Number of filters}=400\times3=1200 \\ \\ \text{ Thus, we can generalize by setting Hour }=x \\ \text{ Number of filters}=400\times x=400x \end{gathered}$

- Comparing this with the general equation, we have:

$\begin{gathered} y=400x \\ y=mx+c \\ \\ m=400 \end{gathered}$

- The slope of the second equation is 400

Final Answer

The slope of the second equation is greater with a value of 400