We write pattern linear function
f(x) = ax + b
Both points must be in one straight line so they can be used to lay the system of equations .
Points A=(4,4), B = (-1,5)
x y x y
[tex] \left \{ {{f(x)=ax + b (Point A)} \atop {f(x) = ax +b (PointB)}} \right. \\ \\ \left \{ {{4 =a*4 + b} \atop {5=a*(-1)+b}} \right. \\ \\ \left \{ {{b= 4 -4a} \atop {5 = -a + (4 - 4a)}} \right. \\ \\ \left \{ {{b = 4 - 4a} \atop {5 - 4 = - 5a }} \right. \\ \\ \left \{ {{b = 4 - 4a} \atop {a = - \frac{1}{5} }} \right. \\ \\ \left \{ {{ b = 4 - 4*(- \frac{1}{5} )= 4 + \frac{4}{5} = 4,8} \atop {a = - \frac{1}{5} }} \right. [/tex]
We insert the calculated a and b in the equation f(x) = ax + b
[tex]y = - \frac{1}{5} x + 4,8[/tex]
Since a> 0, the function is decreasing
