Answer:
f(x) = 5x - 5
Step-by-step explanation:
Let the equation of the linear function is,
f(x) = mx + b
Here, m = Slope of the graph
b = y-intercept
Slope of the line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
m = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
From the table attached,
Slope of the line passing through (2, 5) and (6, 25) will be,
m = [tex]\frac{25-5}{6-2}[/tex]
m = 5
Equation of the linear function will be,
f(x) = 5x + b
Since, a point (10, 45) lies on the function,
45 = 5(10) + b
b = 45 - 50
b = -5
Equation of the linear function will be,
f(x) = 5x - 5
