Answer:
The slope of the graph of machine 1 is: 1/2
The slope of the graph of machine 2 is: 4/5
Step-by-step explanation:
Machine 1
Machine 1 Table is given by
Time (sec) 1 2 3 4
Amount (gal) 0.5 1 1.5 2
Taking two points
Determining the slope between any two points (1, 0.5) and (2, 1)
[tex]\left(x_1,\:y_1\right)=\left(1,\:0.5\right),\:\left(x_2,\:y_2\right)=\left(2,\:1\right)[/tex]
[tex]m=\frac{1-0.5}{2-1}[/tex]
[tex]m=0.5[/tex]
[tex]m = 1/2[/tex]
Therefore, the slope of the graph of machine 1 is: 1/2
Machine 2
Taking two points from the graph of Machine 2
Determining the between any two points (0, 0) and (10, 8)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(0,\:0\right),\:\left(x_2,\:y_2\right)=\left(10,\:8\right)[/tex]
[tex]m=\frac{8-0}{10-0}[/tex]
[tex]m=\frac{4}{5}[/tex]
Therefore, the slope of the graph of machine 2 is: 4/5
