Answer:
The linear function is: p(x) = 3x+65The linear function is: p(x) = 3x+65
Step-by-step explanation:
Let x be the number of t-shirts and y be the total pay
As we can clearly see in the table that there is a linear relationship between x and y
A linear function is given as:
[tex]y = mx+b[/tex]
Here m is the gradient of the function then
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Taking any two pairs of x and y
(1,68) and (2,71)
[tex]m = \frac{71-68}{2-1}\\m = 3[/tex]
Putting in equation
[tex]y = 3x+b[/tex]
Putting a pair (1,68) in the equation to find the value of b
[tex]68 = 3(1) + b\\68 = 3+b\\b = 68-3\\b = 65[/tex]
Putting the value of b
[tex]y = 3x+65[/tex]
Let p(x) be the linear function
Hence,
The linear function is: p(x) = 3x+65
