1. Sketching Linear Graphs
All sketching methods involves finding two coordinate points that satisfy the rule and drawing a line through these points

2. 4 ways to sketch linear graphs
1. Find any two coordinate pairs by substitution
2. Find y intercept and one other coordinate pair by substitution
3. Find y intercept and x intercept
4. Use y = mx + c form to find y intercept and use gradient to find another point

3. Find any two coordinate pairs by substitution
Given y= 2x - 4
Put x = 1 into the rule
y = 2 x 1 - 4
= -2
Plot ( 1, -2)
Put x = 2 into the rule
y = 2 x 2 - 4
= 0
Plot (2, 0)
Draw a line through these points

4. Advantages and Disadvantages
Quick if you know how to substitute into a rule and plot points
Disadvantages
May not show intercepts with axis
Does not involve understanding of gradient or rate of change

5. Find y intercept and one other coordinate pair by substitution
Given y= -2x + 5
Put x = 0 into the rule
y = -2 x 0 + 5
= 5
Plot y intercept (0, 5)
Put x = 1 into the rule
y = -2 x 1 + 5
= 3
Plot point (1, 3)
Draw a line between the points

6. Advantages and Disadvantages
Identifies the y intercept
Easy to find second point and plot it
Disadvantages
Does not find x intercept
Does not involve understanding of gradient or rate of change

7. Find y intercept and x intercept
Given y = 2x + 4
To find y intercept make x = 0
y = 2 x 0 + 4
= 4
Plot ( 0, 4)
To find x intercept make y = 0
and solve for x :
Plot (-2, 0)
Draw a line through both points

8. Advantages and Disadvantages
Identifies the y intercept
Identifies x intercept
Disadvantages
Does not involve understanding of gradient or rate of change

9. Using y = mx + c form Plot y intercept and use gradient to find another
Given y = 0.5x + 1
y intercept is ( 0, 1) plot this
Identify the gradient = m value
From (0, 1) go across 2 and up 1
and plot a point
Draw a line through the points

10. Advantages and Disadvantages
Identifies y intercept
Shows understanding of gradient , (rate of change)
Disadvantages
Rule must be in
y = mx + c form
Does not find x intercept