y = mx + c
In this activity, you will use applets to explore the effects of gradient and y-intercept on straight lines.
Question 1
What happens when m (the gradient) is positive?
Question 2
What happens when m (the gradient) is negative?
Question 3
What happens when c (the y-intercept) is positive?
Question 4
What happens when c (the y-intercept) is negative?
Question 5
What happens when c (the y-intercept) is zero?
Question 6
Describe the lines where m (the gradient) is zero?
[size=150]Simultaneous Equations[/size]
Question 7
On the graph above, show the graph of y = x + 2. [br][br][i][b]On the same graph[/b][/i], plot the graph of y = 2x - 2[br][br]What do you notice about these lines? Are there any special points for these lines? What are the coordinates of these points?
Solving Simultaneous Equations Graphically
We will use straight line graphs on the same axes to solve simultaneous equations below.
Question 1)
The graph of [math]y+2x=4[/math] has been drawn on the axes below:
(a) On the same grid, draw the graph of [math]y=x+1[/math].
(b) Use the graphs to solve the simultaneous equations:[br][math]y+2x=4[/math][br][math]y=x+1[/math]
Question 2
The straight line [math]y=2x+3[/math] has been drawn on the axes below:
(a) On the same grid, draw the graph of [math]y=-3x+8[/math]
(b) Use the graphs to solve the simultaneous equations:[br][math]y=2x+3[/math][br][math]y=-3x+8[/math]
Question 3
The graph of [math]3x+y=8[/math] has been drawn on the grid below:
(a) On the same grid, draw the graph of [math]x+y=6[/math].
(b) Use the graphs to solve the simultaneous equations:[br][math]3x+y=8[/math][br][math]x+y=6[/math]
Question 4
(a) On the grid below, draw the graphs of these functions:[br][math]y=3x+1[/math][br][math]x+y=7[/math]
(b) Use the graphs you have drawn above to solve the simultaneous equations[br][math]y=3x+1[/math][br][math]x+y=7[/math]
Question 5
(a) On the grid below, draw the graphs of these functions:[br][math]y=3x+5[/math][br][math]x-2y+6=0[/math]
(b) Use the graphs you have drawn above to solve the simultaneous equations[br][math]y=3x+5[/math][br][math]x-2y+6=0[/math]