GRAPHING LINEAR FUNCTIONS
Graphing Straight Lines
This presentation looks at two methods for graphing a line.
1. By finding and plotting points
2. Using the gradient and the y-intercept where y = mx + b
m is the gradient
b is the
y-intercept
1. Graphing Straight Lines by plotting points
y = 2x – 1 y
x1 2 3 4 5-1-2-3
123456
-1-2-3-4
Choose values for x and find the corresponding value for y
x = 1, y = 2(1) - 1 = 1 •
x = 2, y = 2(2) - 1 = 3
•
x = -1, y = 2(-1) - 1 = - 3 •
Connect the points
This information is often presented in table form
xy
11
23
–1–3
y = – x + 2 y
x1 2 3 4 5-1-2-3
123456
-1-2-3-4
Choose values for x and find the corresponding value for y
x = 1, y = -(1) +2 = 1 •
x = 2, y = -(2) +2 = 0 •
x = -1, y = -(-1) +2 = 3
•
x = 3, y = -(3) +2 = -1
•
Connect the points
1. Graphing Straight Lines by plotting points
2. Graphing Straight Lines by using the gradient and the y-intercept
y
x1 2 3 4 5-1-2-3
123456
-1-2-3-4
•
y = 2x – 3
m =
y-intercept =
2
– 3
Place a point at the y-intercept
•A gradient of 2 is a rise of 2 over a run of 1
This gives us the point (1, –1)
Connect the points
2. Graphing Straight Lines by using the gradient and the y-intercept
y
x1 2 3 4 5-1-2-3
123456
-1-2-3-4
•
y = – 4x + 2
m =
y-intercept =
– 4
2
Place a point at the y-intercept
•
A gradient of –4 is a drop of 4 over a run of 1
This gives us the point (1, –2)
Connect the points
2. Graphing Straight Lines by using the gradient and the y-intercept
y
x1 2 3 4 5-1-2-3
123456
-1-2-3-4 •
y = – x – 3
m =
y-intercept =
– 1
– 3
Place a point at the y-intercept
•A gradient of –1 is a drop of 1 over a run of 1
This gives us the point (1, –4)
Connect the points
2. Graphing Straight Lines by using the gradient and the y-intercept
y
x1 2 3 4 5-1-2-3
123456
-1-2-3-4
•m =
y-intercept = 2
Place a point at the y-intercept
•
This gives us the point (3, 4)
Connect the points
23
2 xy
3
2
A gradient of is a rise of 2 over a run of 3
3
2
Re-arranging equations to read the gradient and the y-intercept
Remember the general form of a straight line is y = mx + b
7 yxExample 1 Subtract x from both sides
xy 7 Rearrange so that the x term is first
7 xy
Therefore, the gradient is – 1 and the y-intercept is 7.
y = mx + b
23 yxExample 2 Subtract 3x from both sides
xy 32 Rearrange so that the x term is first
23 xy
Therefore, the gradient is – 3 and the y-intercept is – 2
y
x1 2 3-1-2-3-4
12345
-1-2-3-4-5
•
•
y = mx + b
14 yxExample 3 Subtract 4x from both sides
xy 41 Rearrange so that the x term is first
14 xy
Therefore, the gradient is 4 and the y-intercept is – 1
y
x1 2 3-1-2-3-4
12345
-1-2-3-4-5
•
•
Multiply both sides by – 1
14 xy
y = mx + b
52 xyExample 4 Add x to both sides
xy 52 Rearrange so that the x term is first
52 xy
y
x1 2 3 4-1-2-3
1
2
3
4
5
-1
-2
••
Divide both sides by 2
2
5
2
1 xy
Therefore, the gradient is
and the y-intercept is 2.52
1
y = mx + b
823 xyExample 5 Add 2x to both sides
xy 283 Rearrange so that the x term is first
823 xy
y
x1 2 3 4-1-2-3
1
2
3
4
5
-1
-2
•
•
Divide both sides by 3
3
8
3
2 xy
Therefore, the gradient is and
the y-intercept is 3
2
3
8
y = mx + b
624 yxExample 6 Subtract 4x from both sides
xy 462 Rearrange so that the x term is first
642 xy
y
x1 2 3 4-1-2-3
1
2
3
4
5
-1
-2
•
•
Divide both sides by 2
32 xy
Therefore, the gradient is – 2 and the y-intercept is 3
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