Welcome to calculating slope from a graph! Slope tells us how steep a line is. It's calculated as the ratio of rise over run - that's the vertical change divided by the horizontal change between any two points on the line. Let's see how this works with a practical example.
The first step in calculating slope is to choose two clear points on the line. Look for points where the line crosses grid intersections, as these give us exact coordinates that are easy to read. For our example, I'll select point 1 at coordinates (1, 1.5) and point 2 at coordinates (4, 3). These points are clearly visible and have precise coordinates.
Now let's calculate the rise, which is the vertical change between our two points. Rise equals y₂ minus y₁. Using our points, that's 3 minus 1.5, which equals 1.5. This means the line goes up 1.5 units vertically from the first point to the second point. You can see this vertical distance highlighted in green.
Next, we calculate the run, which is the horizontal change between our two points. Run equals x₂ minus x₁. Using our coordinates, that's 4 minus 1, which equals 3. This means we move 3 units horizontally to the right from the first point to reach the same horizontal level as the second point. The horizontal distance is shown in orange.
Finally, we calculate the slope by dividing rise by run. The slope formula is m equals rise over run, or y₂ minus y₁ over x₂ minus x₁. Substituting our values: m equals 1.5 over 3, which equals 0.5. This means our line has a slope of 0.5, indicating that for every 1 unit we move horizontally to the right, the line rises 0.5 units vertically. This completes our slope calculation from the graph!