Find the linear-to-linear function who graph passes through the points (1,1) (5,2) and (20,3). I know the function is y=ax+b/x+d. I need help getting it to that form.

To find the linear-to-linear function in the form y = ax + b / x + d, we need to follow these steps:

Step 1: Find the value of a
We can begin by using the two given points (1,1) and (5,2).
Let's substitute these points into the formula: y = ax + b / x + d.

For point (1,1):
1 = a(1) + b / (1) + d
1 = a + b + d (1)

For point (5,2):
2 = a(5) + b / (5) + d
2 = 5a + b + d (2)

Step 2: Solve for a
To eliminate b and d from equations (1) and (2), we can subtract equation (1) from equation (2).

(2) - (1) gives us:
2 - 1 = 5a - a + b - b + d - d
1 = 4a

So, a = 1/4.

Step 3: Find b and d
Since we found the value of a, we can substitute it back into equation (1) (or (2)) to solve for b and d.

Using equation (1):
1 = (1/4) + b + d
1 - 1/4 = b + d
3/4 = b + d (3)

Step 4: Substitute values into the equation
Now that we have the values of a, b, and d, we can write the linear-to-linear function in the form y = ax + b / x + d.

Using the values we found:
y = (1/4)x + (3/4) / x + d

Since d is equal to 3/4, we can substitute it:
y = (1/4)x + (3/4) / x + 3/4

Therefore, the linear-to-linear function that passes through the points (1,1), (5,2), and (20,3) is:
y = (1/4)x + (3/4) / x + 3/4.

To find the linear-to-linear function in the form y = (ax + b)/(x + d) that passes through the given points (1,1), (5,2), and (20,3), we can use the following steps:

Step 1: Set up the general equation of the linear-to-linear function as y = (ax + b)/(x + d).

Step 2: Plug in the x and y coordinates of each given point into the equation to set up a system of equations.

Let's start with the first point (1,1):
1 = (a * 1 + b)/(1 + d) --> Equation 1

Now, let's move on to the second point (5,2):
2 = (a * 5 + b)/(5 + d) --> Equation 2

Finally, we'll use the third point (20,3):
3 = (a * 20 + b)/(20 + d) --> Equation 3

Now we have a system of three equations (Equations 1, 2, and 3) with the variables a, b, and d. Solving this system of equations will give us the values of a, b, and d, which will allow us to write the function in the desired form.

At this point, we will proceed with solving the system of equations.