Transformations can really help us understand linear equations better. They do this by showing us what these equations look like in a more visual way. Here are some important transformations:
Shifts: If we move the graph up or down by units, the new equation looks like this: .
Reflections: When we flip the graph over the x-axis, the equation changes to .
Scaling: If we change how steep the line is, the slope will be different. For example, is steeper than .
These transformations make it easier to see different types of solutions. They help us find important points on the graph, like where lines cross each other or how parallel lines act differently.
Transformations can really help us understand linear equations better. They do this by showing us what these equations look like in a more visual way. Here are some important transformations:
Shifts: If we move the graph up or down by units, the new equation looks like this: .
Reflections: When we flip the graph over the x-axis, the equation changes to .
Scaling: If we change how steep the line is, the slope will be different. For example, is steeper than .
These transformations make it easier to see different types of solutions. They help us find important points on the graph, like where lines cross each other or how parallel lines act differently.