Question

Write an equation for the function of the table.write an equation for the original line on the grid.

Answer 1

We need to write teh equation for the line represented in the table, so we can take two any points from the table, we choose (0,20) and (8,0), so:

`\begin{gathered} \text{The equation of a line with two points is:} \\ P_1=(t_1,V_1)=(0,20) \\ P_2=(t_2,V_2)=(8,0) \\ V-V_1=(V_2-V_1)/(t_2-t_1)(t-t_1) \\ V-20=(0-20)/(8-0)(t-0) \\ V=-(20)/(8)t+20 \\ V=-(5)/(2)t+20 \end{gathered}`

And the equation for the original line we can take two points from the graph, we choose (1, 25) and (2, 15), so:

`\begin{gathered} P_1=(1,25),P_{}=(2,15) \\ V-25=(15-25)/(2-1)(t-1) \\ V=-(10)/(1)(t-1)+25 \\ V=-10t+10+25 \\ V=-10t+35 \end{gathered}`