Gradient of a line 2
Below is a blue line with its equation, and a calculation of the gradient of the line.
Can you work out where the gradient comes from? (Hint: look at the green triangle)
Predict what will happen to the gradient when you move the red points up and down the blue line.
red points up and down the blue line. Was your prediction correct? If not, what do you notice now?
Can you explain what has happened to the gradient?
How does m affect the gradient of the blue line?
How does c affect the gradient of the blue line?
Use what you have discovered so far to predict the gradient of each of the following equations. Then use the sliders to check your answers.
1. y = 2x - 3
2. y = 0.5x + 5
3. y = -3x + 1
This could make for an excellent homework for students, who have to come in and explain their findings the following lesson, or write them up in a report.
You can use this at the front of the classroom by changing the values of m and c to create different lines and ask the pupils for the gradient (to get rid of the green triangle and gradient, just place the two red points over each other).