Sketching Linear Graphs

All sketching methods involves finding two

coordinate points that satisfy the rule and drawing a line through these points

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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

Find any two coordinate pairs by substitution

• Given y= 2x - 4

Put x = 2 into the rule y = 2 x 2 - 4 = 0

Put x = 1 into the ruley = 2 x 1 - 4 = -2 Plot ( 1, -2)

Plot (2, 0)

Draw a line through these points

Advantages and Disadvantages

Advantages

• 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

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

Advantages and Disadvantages

Advantages

• 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

Find y intercept and x interceptGiven 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 :

x

x

x

x

x

22

2

2

4

24

44240

420

Plot (-2, 0)

Draw a line through both points

Advantages and Disadvantages

Advantages

• Identifies the y intercept

• Identifies x intercept

Disadvantages

• Does not involve understanding of gradient or rate of change

Using y = mx + c form Plot y intercept and use gradient to find

another• Given y = 0.5x + 1y intercept is ( 0, 1) plot this

Identify the gradient = m value

run

risem

2

15.0

From (0, 1) go across 2 and up 1

and plot a point

Draw a line through the points

Advantages and Disadvantages

Advantages

• Identifies y intercept

• Shows understanding of gradient , (rate of change)

Disadvantages

• Rule must be in

y = mx + c form

• Does not find x intercept