powerpoint presentation

2. LET’S LEARN
A linear function usually takes the form
f(x) = mx + b
where m and b are constants
This equation is in function notation and should be read
simply as “f of x” or “a function of x into y.” We can also used
other letters to represent a function. Letters g and h are
commonly used.
Take note that that y= f(x), and a linear function also
takes the form y = mx + b. The graph of linear function is
always a straight line.

3. A linear function is a first-degree function where the
standard form is written in the form of
ax + by = c
where a, b , and c are integers, and a > 0.
A linear function comes in the form f(x) = mx + b or y =
mx + b. This form is referred to as the slope-intercept form
where m is the slope of the line and b represents the y-
intercept of the linear function.
y= mx + b
y = 2x – 1 2x - 3y = 8
y = 3x + 4 x + 5y = 5

4. Writing linear function from slope Intercept form (y =
mx + b) to standard form (ax + by = c) :
Example 1. y = 5x - 4 Example 2. y = 4x + 1
-5x + y = -4
-1[-5x + y] = -4(-1)
5x – y = 4
or
−5𝑥+𝑦
−1
=
−4
−1
= 5x – y = 4
-4x + y = 1
-1(-4x + y = 1(-1)
4x – y = -1
or
−4𝑥+𝑦
−1
=
1
−1
= 4x – y = -1

5. Example 3. y = -
𝟑
𝟐
x + 6 Example 4. y =
𝟑
𝟓
x - 1
y = -
𝟑
𝟐
x + 6
3
2
x + y = 6
2
3
2
𝑥 + 𝑦 = 6
2
3
2
𝑥 + (2)(y) = 6(2)
3x + 2y = 12
y =
𝟑
𝟓
x - 1
-
3
5
x + y = -1
5 −
3
5
x + y = −1
5(-
3
5
x) + (5)(y) = (-1)(5)
-3x + 5y = -5
-1(-3x + 5y = -5) = 3x - 5y = 5

6. Linear function from standard form (ax + by = c) to slope-
intercept form (y = mx + b):
Example 1. 12x – 4y = 9 Example 2. x + y = 5
12x – 4y = 9
-4y = -12x + 9
−4𝑦
−4
=
−12𝑥
−4
+
9
−4
y = 3x -
𝟗
𝟒
-x + y = 5
y = -x + 5

7. Example 1. 2x = y - 4 Example 2. 3y = 3 – 2x
(y = mx + b form)
2x = y – 4
-y = -2x – 4
−𝑦
−1
=
−2𝑥 −4
−1
; y = 2x + 4
y = mx + b is the same as mx +
b = y,
It is also equal to 2x + 4 = y
(ax + by = c form)
3y = 3 – 2x
2x + 3y = 3
Writing linear function into y = mx + b form and ax + by
= c form.