Exploring gradients and intercepts
- Author:
- Barry Williams
y = mx + b
1. Using the applet below input the above equation using the value 0 for m
2. Keep increasing the value of m to larger positive values, observe what happens to the graph
Equation y = mx + b
Write a sentence about the effect that the value of m has on the graph of the straight line y = mx -5
Now try varying the value of b. First set the value of m = 1, so that you will be graphing y = x + b
Increase the value of b from -5 and see what happens to the graph
What is the y-intercept when b = -5
What is the y intercept when b = 0
What is the y-intecept when b = 5
What effect does b have on the graph of the straight line y = x + b
Describe the differences between y = 2x + 3 and y = -2x + 3 and y = 3x + 2 and y = 3x -2 (predict before graphing)
Sketch the following graphs in your math book, use geogebra to check your answers
y = x y = -2x
y = y =
y = -x + 3 y = 3x - 4
y = y =
White a summary sentence describing how to sketch y = mx + b when given the values of m and b
Sketch the following
y = -3 y = 4
y = 0 y =
x = -2 x = 3
x = 0 x = -
Graph y = 2( x+ 3) and y = 2x + 6
How many lines can you see?
What is the gradient for y = 2(x + 3)
What is the y-intercept for y = 2(x + 3)
Predict the out come of the following 2 graphs y = 3(2x + 1) and y = 6x +3
Taking it further
Write 3 equations that will give parallel graphs
Graph them
Write 3 equations that all have the same y intercept
Graph 3 lines with same y intercept
Write 3 equations that are parallel to the x axis
Graph parallel to x axis
Write 3 equations that will give graphs that are parallel to the y axis