Exploring Slope and Y-Intercept

Use this applet to explore how slope and y-intercept affect the graph of a straight line.

y = 1x + 0

How to Use This Applet

1. Move the Slope (m) slider to change the steepness and direction of the line.
2. Move the Y-Intercept (b) slider to change where the line crosses the y-axis.
3. Observe how the graph and equation change as you move the sliders.
4. Try positive, negative, and zero values for both m and b.
5. Click Reset Graph to return to the original equation y = x.
6. Click Show Slope Triangle to display the rise and run of the line.
7. Observe the slope calculation below the graph to understand how rise divided by run gives the slope.
8. Click Hide Slope Triangle to remove the triangle from the graph.

Explore and Investigate

1. Set the y-intercept to 0. Change the slope from -3 to 3. What happens to the direction and steepness of the line?
2. Set the slope to 2. Change the y-intercept from -4 to 4. What changes about the graph? What stays the same?
3. Set the slope to 0. Move the y-intercept slider. What do you notice about the line? Explain why this happens.
4. Find two different equations whose graphs are parallel. What do their slopes have in common?
5. Set the slope to 3 and click Show Slope Triangle. Observe the rise and run. Now change the slope to -3. What changes about the triangle? How does this help explain positive and negative slopes?