When we talk about the slope-intercept form of a line, we mean the equation (y = mx + b).

Here, (m) is the slope, and (b) is the y-intercept.

To really understand how the slope and y-intercept work, you need to know how they change the graph of the line.

Slope ((m))

The slope shows how steep the line is and which way it goes.

• If (m) is positive, the line goes up from left to right.
• If (m) is negative, the line goes down from left to right.

Example 1:

In the equation (y = 2x + 1), the slope is 2.

This means that for every time you move 1 unit to the right, the line goes up 2 units.

Example 2:

If we change the slope to (y = -2x + 1), now the slope is -2.

That means if you move 1 unit to the right, the line goes down 2 units.

Y-Intercept ((b))

The y-intercept is where the line crosses the y-axis.

This number can move the line up or down without changing its steepness.

Example 1:

In the equation (y = 3x + 2), the line crosses the y-axis at the point (0, 2).

Example 2:

If we change the y-intercept to (y = 3x - 1), the line crosses at (0, -1).

The slope is still the same, but now the line has moved down.

Summary

• Changing the slope ((m)) changes how steep the line is and the direction it's going.
• Changing the y-intercept ((b)) simply moves the line up or down without changing how steep it is.

By changing (m) and (b), you can create different lines. This helps you represent all sorts of situations using linear equations!