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Hey there! Let's explore how things change and learn how to measure the steepness of a line.
Slope is a measure of steepness. It tells us how much a vertical change relates to a horizontal change.
We often call slope the 'rate of change' or 'rise over run'. It compares the vertical change to the horizontal change.
To find the slope, we divide the change in y (rise) by the change in x (run). A steeper line has a larger slope value.
✏️ Worked example
Find the slope of the line that passes through the points (2, 3) and (5, 9).
- Identify the coordinates: (x₁, y₁) is (2, 3) and (x₂, y₂) is (5, 9).
- Find the vertical change (rise) by subtracting the y-values: 9 - 3 = 6.
- Find the horizontal change (run) by subtracting the x-values: 5 - 2 = 3.
- Divide the rise by the run: 6 / 3 = 2.
- The slope of the line is 2. This means the line goes up 2 units for every 1 unit it moves to the right.
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