Vertical and horizontal shifts are important when we look at linear graphs. They change how the graph looks and where it is on the chart.

1. Vertical Shifts:
When you add or subtract a constant number, let's call it $k$, to the equation $y = mx + b$, you move the graph up or down.
For example, if $k$ is 3, you move the line up by 3 units. So, the equation would change like this:
From $y = mx + b$ to $y = mx + (b + k)$.

2. Horizontal Shifts:
If you add or subtract a number to $x$, the graph shifts left or right.
For instance, in the equation $y = m(x - h) + b$, if $h$ is positive, the graph moves to the right by $h$ units.

Example:

• Start with the original equation: $y = 2x + 1$
• For a vertical shift (up 3): the new equation is $y = 2x + 4$
• For a horizontal shift (right 2): the new equation becomes $y = 2(x - 2) + 1$

These changes help us see how linear functions behave and understand their shapes better!