To create a rectangle using the linear equation \( y = mx + b \), we can define the rectangle based on two opposing sides. Let's assume we want to create a rectangle with the following vertices:
- Bottom-left corner
(x1, y1) - Bottom-right corner
(x2, y1) - Top-left corner
(x1, y2) - Top-right corner
(x2, y2)
For simplicity, let's say:
x1 = 1,y1 = 2(bottom-left corner)x2 = 5,y1 = 2(bottom-right corner)x1 = 1,y2 = 6(top-left corner)x2 = 5,y2 = 6(top-right corner)
Now, we need to find the linear equations for the top and bottom sides of the rectangle.
Bottom Side
We will use the coordinates of the bottom side (x1, y1) to (x2, y1):
- Bottom side: \( y = 2 \)
- Here \( m = 0 \) (slope is zero since it's a horizontal line), and \( b = 2 \).
The equation for the bottom side is: \[ y = 0x + 2 \] or simply, \[ y = 2 \]
Top Side
For the top side, it will have the same slope and be at \( y = 6 \):
- Top side: \( y = 6 \)
The equation for the top side is: \[ y = 0x + 6 \] or simply, \[ y = 6 \]
Summary of the Rectangle
-
Vertices:
- Bottom-left:
(1, 2) - Bottom-right:
(5, 2) - Top-left:
(1, 6) - Top-right:
(5, 6)
- Bottom-left:
-
Equations:
- Bottom Side: \( y = 2 \)
- Top Side: \( y = 6 \)
You can replicate this method with different values for the coordinates to create various rectangles. Adjust the \( y1 \) and \( y2 \) values to change the height, and adjust \( x1 \) and \( x2 \) values to change the width.