Slope measures how steep a line is. It represents the rate of change between two variables. We can visualize slope as rise over run - the vertical change divided by the horizontal change between any two points on the line.
To find slope from two points, we use the formula: m equals y2 minus y1, divided by x2 minus x1. Let's work through an example with points (1, 2) and (4, 8). The rise is 8 minus 2, which equals 6. The run is 4 minus 1, which equals 3. So the slope is 6 divided by 3, which equals 2.
We can find slope directly from equations. In slope-intercept form y equals mx plus b, the coefficient m is the slope. For standard form Ax plus By equals C, the slope is negative A divided by B. For example, with 3x plus 2y equals 8, we solve for y to get y equals negative 1.5x plus 4, so the slope is negative 1.5.
There are four types of slopes. Positive slope means the line rises from left to right. Negative slope means the line falls from left to right. Zero slope creates a horizontal line. Undefined slope occurs with vertical lines, where we divide by zero in our slope formula.
Let's practice with a problem. Find the slope between points negative 1, 2 and 3, negative 4. Using our formula, we substitute the values: slope equals negative 4 minus 2, divided by 3 minus negative 1. This gives us negative 6 divided by 4, which equals negative 1.5. The negative slope confirms our line falls from left to right.