Answer:
Observe the attached image
Step-by-step explanation:
We have the graph of a line that passes through the points (0,5) and (2, 1).
The equation of the line that passes through these points is found in the following way:
[tex]y = mx + b[/tex]
Where
m = slope
[tex]m = \frac {y_2-y_1}{x_2-x_1}\\\\m = \frac{1-5}{2-0}\\\\m = -2\\\\b = y_2-mx_2\\\\b = 1 -(-2)(2)\\\\b = 5[/tex]
So
[tex]y = -2x + 5[/tex]
We must apply to this function the transformation[tex]f (x-4)[/tex].
We know that a transformation of the form
[tex]y = f (x + h)[/tex] shifts the graph of the function f(x) h units to the right if [tex]h <0[/tex], or shifts the function f(x) h units towards the left if [tex]h> 0[/tex].
In this case [tex]h = -4 <0[/tex] then the transformation [tex]f(x-4)[/tex] displaces the graph 4 units to the right.
Therefore if f(x) passes through the points (0,5) and (2,1) then [tex]f (x-4)[/tex] passes through the points (4, 5) (6, 1)
And its equation is:
[tex]y = -2(x-4) +5\\\\y = -2x +13[/tex]
Observe the attached image
