Transformations are really important for understanding linear equations, like how steep a line is and where it starts on a graph. Let’s break it down:
Shifts: When we change the equation from (y = mx + b) to (y = mx + b + k), we move the graph up or down by (k). This means the starting point on the y-axis changes, but how steep the line is (the slope, or (m)) stays the same.
Reflections: If we have an equation like (y = -mx + b), a reflection across the x-axis flips the slope to its opposite. This shows how the slope is connected to the direction of the line.
For example, if we take the equation (y = 2x + 3), the slope is 2, which means the line goes up two units for every one unit it goes to the right. The intercept, or where it crosses the y-axis, is 3.
Now, if we change it to (y = 2x + 5), the slope still stays 2, but the intercept changes to 5.
This shows us how transformations help us see important parts of linear equations!
Transformations are really important for understanding linear equations, like how steep a line is and where it starts on a graph. Let’s break it down:
Shifts: When we change the equation from (y = mx + b) to (y = mx + b + k), we move the graph up or down by (k). This means the starting point on the y-axis changes, but how steep the line is (the slope, or (m)) stays the same.
Reflections: If we have an equation like (y = -mx + b), a reflection across the x-axis flips the slope to its opposite. This shows how the slope is connected to the direction of the line.
For example, if we take the equation (y = 2x + 3), the slope is 2, which means the line goes up two units for every one unit it goes to the right. The intercept, or where it crosses the y-axis, is 3.
Now, if we change it to (y = 2x + 5), the slope still stays 2, but the intercept changes to 5.
This shows us how transformations help us see important parts of linear equations!