The slope of a line is shown by the letter ( m ).

You can think of the slope as how steep the line is.

It is found by looking at how much the line goes up (rise) compared to how far it goes sideways (run).

We can write this as:

[ m = \frac{\text{rise}}{\text{run}} ]

Then, there’s the angle of the line, which we call ( \theta ).

We can use something called the tangent function to figure it out:

[ \tan(\theta) = m ]

This means that the slope affects the angle of the line.

Let’s break down what happens with different slopes:

• If the slope is positive (( m > 0 )), the line goes up as it moves from left to right. The angle ( \theta ) is between ( 0° ) and ( 90° ).

• If the slope is negative (( m < 0 )), the line goes down from left to right. The angle ( \theta ) is between ( -90° ) and ( 0° ).

• If the slope is zero (( m = 0 )), the line is flat and horizontal, at ( 0° ).

• As the slope ( m ) gets bigger, the angle ( \theta ) gets closer to ( 90° ).

So, we can see how slope and angle are connected in straight lines on a graph.