Given:
Find-: Graph and rate of change.
Sol:
Rate of change :
The rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.
[tex]\text{ Slope = }\frac{y_2-y_1}{x_2-x_1}[/tex]
Where,
[tex]\begin{gathered} (x_1,y_1)=(1,1.25) \\ \\ (x_2,y_2)=(2,2.4) \end{gathered}[/tex]
So the slope is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{2.4-1.25}{2-1} \\ \\ m=1.15 \end{gathered}[/tex]
The general form of the equation is:
[tex]\begin{gathered} y=mx+c \\ \\ y=1.15x+c \end{gathered}[/tex]
The value of "c" is:
[tex]\begin{gathered} (x,y)=(1,1.25) \\ \\ y=1.15x+c \\ \\ 1.25=1.15(1)+c \\ \\ c=1.25-1.15 \\ \\ c=0.10 \end{gathered}[/tex]
So equation of a line is:
[tex]\begin{gathered} y=mx+c \\ y=1.15x+0.10 \end{gathered}[/tex]
The graph of the line is:
