Given:
During the first year of opening his law firm, a lawyer served 36 clients.
In the second year, his number of clients grew to 44.
Let the number of clients = c, and the number of years = t
There is a linear relationship between c and t
We will find the equation that relates (c) and (t)
So, when t = 1, c = 36
and when t = 2, c = 44
The equation will take the general slope-intercept form
c = m * t + b
Where m is the slope, and b is the y-intercept
The slope will be calculated as follows:
[tex]m=\frac{44-36}{2-1}=\frac{8}{1}=8[/tex]So, the equation will be: c = 8t + b
using the first condition to find (b)
[tex]\begin{gathered} 36=8\cdot1+b \\ b=36-8=28 \end{gathered}[/tex]So, the answer will be the equation will be:
[tex]c=8t+28[/tex]