Show the slope of 6 on a graph

Answer 1

To represent a slope of 6 on a graph, you can visualize it as a line that rises 6 units vertically for every 1 unit it runs horizontally.

Here's a step-by-step guide on how to create the graph:

1. Draw the Axes:

   • Draw a horizontal line (x-axis) and a vertical line (y-axis) intersecting at the origin (0,0).

2. Plot a Point:

   • Start at the origin (0,0).

3. Using the Slope:

   • From the origin, move 1 unit to the right along the x-axis. This represents the horizontal change (\(\Delta x = 1\)).
   • From that point, move 6 units up. This represents the vertical change (\(\Delta y = 6\)).
   • The new point will be at (1, 6).

4. Draw the Line:

   • Use a ruler to draw a straight line through the points (0,0) and (1,6). This line represents a slope of 6.

The slope (m) can generally be expressed as: \[ m = \frac{\Delta y}{\Delta x} \] For this line: \[ m = \frac{6}{1} = 6 \]

Summary

• Starting Point: (0, 0)
• Second Point: (1, 6)
• Slope: 6 (rise over run)

If you were to sketch this on graph paper or using graphing software, you'd see a steep line inclined towards the top right as it demonstrates the steep slope of 6.