# Equation for a line through (4,5) with y-intercept 2

- Author:
- Sybilla Beckmann

- Topic:
- Equations

How can we derive and explain an equation for the line through (4,5) with y-intercept 2? This applet will help you develop an equation using a variable-parts perspective.

1) Initially, the 4 horizontal parts and 3 vertical parts are all 1 centimeter long. When you move the slider, the parts will stay the same size as each other, but that size changes. Predict what will happen to the point (x,y).
2) Consider the 4 horizontal parts to be 1 group of size x centimeters. How many of these groups are in the 3 vertical parts? Does it depend on how long the parts are in centimeters?
3) Use part 2 to describe the total length of the 3 vertical parts in terms of x. Write a multiplication equation that uses our definition of multiplication.
4) Describe y in terms of the vertical parts. Then use that description and part to find an equation expressing y in terms of x.