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•What is Linear Function?
How to graph a linear function without computer?
Linear Functions with m=2
Linear Functions with m=1
Linear Functions with m=0

•Linear Function:

𝑦 = 𝑚𝑥 + 𝑏

a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero
or one
For example:

𝑦 = 2𝑥 + 1

m=2 and

b=1

𝑦 = 𝑚𝑥 + 𝑏
the slope of the line

How to graph a linear function without computer?
to graph a line, we just need any two points on it
...


X

Y

0

1

1

3

(𝟏, 𝟑)

?

𝑦 =2 1 +1=𝟑

(𝟏, 𝟑)

-2

(𝟎, 𝟏)
1

2

•Linear Function: f(x) = mx + b

𝑦 = 2𝑥 + 1
To find the slope (m) from the graph, do the following:

𝑦1 = 1

𝑦2 = 3

𝑥1 = 0

(𝟏, 𝟑)

3
2
1

(𝟎, 𝟏)

𝑥2 = 1
-1

𝑦2 − 𝑦1 3 − 1
𝑚=
=
=2
𝑥2 − 𝑥1 1 − 0

-2

1

2

•Linear Function: f(x) = mx + b
Let’s graph these functions: Linear Functions with m=2 What happens if we change b

𝑦 = 2𝑥

𝑦 = 2𝑥 + 1

𝑦 = 2𝑥 − 1

•Linear Function: f(x) = mx + b
Now let's compare the three lines:

When b is zero, it means that the line passes through the coordinate origin

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