Answer:
[tex]y = 1.67x[/tex]
Step-by-step explanation:
Function A:
x || 3 || 6 || 9 || 12 || 15
y || 5 || 10 || 15 || 20 || 25
See attachment for Function B
First, we need to determine the equation of function A using linear interpolation
As follows:
[tex]y = y_1 + (x - x_1)\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Take any two corresponding values of x and y to be:
[tex](x_1,y_1) = (3,5)[/tex]
[tex](x_2,y_2) = (15,25)[/tex]
The equation becomes:
[tex]y = y_1 + (x - x_1)\frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]y = 5 + (x - 3)\frac{25 - 5}{15 - 3}[/tex]
[tex]y = 5 + (x - 3)\frac{20}{12}[/tex]
[tex]y = 5 + (x - 3)\frac{5}{3}[/tex]
Open bracket
[tex]y = 5 + \frac{5x}{3} - \frac{5*3}{3}[/tex]
[tex]y = 5 + \frac{5x}{3} - 5[/tex]
Collect Like Terms
[tex]y = \frac{5x}{3} - 5 + 5[/tex]
[tex]y = \frac{5x}{3}[/tex]
[tex]y = 1.67x[/tex]
This function is linear and there is no need to check for function B
