The document provides instruction on linear functions and how to find the x-intercept and y-intercept of a linear equation. It discusses writing linear equations in function notation as f(x), defines the x-intercept as where the graph crosses the x-axis (y = 0) and the y-intercept as where it crosses the y-axis (x = 0). It gives the formula for linear equations in standard form and shows how to set x = 0 and y = 0 to find the intercepts. Examples are worked out, showing how to graph the line based on the intercepts. Classwork assignments are noted at the end.

1. Today
 Warm Up: (3)
 Review Last Khan Academy Topic
 Function Notation: f(x)
 Finding the x and y Intercepts
 Class Work 3.5 Distributed

2. Write the rule for the function graphed below
Warm Up

3. Write the rule for the function graphed below
Warm Up
Y = 2x + 1

5. Function Notation:f(x)..g(x)..h(x)
A function rule is written with two variables, x and y.
It can also be written in function notation, f(x). The f(x), or g(x),
is simply a notation for the dependent variable.
Functions that can be written as equations can be written in
function notation. The variable y and the term f(x) represent the
dependent variable.
It is simply a way to show that the y variable is a function of,
or depends on x. It is read "f at x"
Since x can be any number, the f(x) is the output, (the
dependent variable), when a number is substituted for x.
If used on the same graph, different functions have different
function notations f(x) or g(x) to avoid confusion, but both
represent the y variable.

6. ……….
h(x)= -x + 2g(x)= 2x -1

7. Graphs of Linear
Equations

8. 8
Graphs of y = b
Where b is any number
y = b are always horizontal
lines, and are functions
Graphs of x = a
Where a is any number
x = a are always vertical lines,
and are not functions

9. 9
Graphs of y = mx
y = "a number times x"
y = mx lines will always go through the
origin, and will be at the angle shown.
Graphs of y = mx + c
y = "a number times x plus c"
y = mx + c are similar in shape to y = mx,
but do not go through the origin.

10. 10
Defining Linear Equations
HOW DO I KNOW IF AN EQUATION IS LINEAR?
If an equation is linear, the result is a straight line.
A line can be a function, and not be a linear function.

11. 11
Solutions to Linear Equations
To ask "Is the ordered pair (1,3) a solution to the equation y = 10x - 7?",
is the same as asking, " Is the point (1,3) on the line of y = 10x -7"?
How do we know?
Determine whether the following ordered pairs are solutions
to the equation y = 10x -7 a. (1,3) b. (2, 13) c. (-1,-3)

12. 12
These are the x- and y-Intercepts
The x-intercept is where the graph
crosses the x-axis.
The y-coordinate is always zero.
The y-intercept is where the graph
crosses the y-axis.
The x-coordinate is always zero.
(2, 0)
(0, -6)Being able to locate the intercepts
makes it easy to draw the line
associated with the given equation.

13. Formulas:
Standard Form of a linear equation: Ax + By = C
A, B, & C are all constants and..
a.) A and B are not both zero.
b.) The largest exponent is not greater than 1
Change to Standard Form:
4y + 12 = 6x
The Standard Form of a linear equation
is used when you want to find the
intecepts of a line

14. Formulas: Standard Form of a linear equation: Ax + By = C
The 'x' variable is first..
We use our knowledge of coordinate values and intercepts to find
where (if) the line crosses both axes. Not all lines cross both axes.
The Standard Form of 4y + 12 = 6x is..
At the x intercept, y is always zero. The ordered pair is (x, 0).
6x - 4y = 12
The equation to find the x intercept then, is 6x - 4(0) = 12.
6x = 12, x = 2. The x intercept
coordinates are (2,0)
Find the y intercept. 6(0) -4y = 12
y = -3 The y intercept
coordinates are (0,-3)
Graph the intercepts and
draw the line

15. 15
To find the x-intercept: Plug in 0 for y since y is always 0 at
the x-intercept.
x - 2(0) = 12
x = 12; (12, 0)
y-intercept: Plug in 0 for x.
0 - 2y = 12
y = -6; (0, -6)
Find the x- and y-intercepts.
1. x - 2y = 12

17. 𝟗
𝟓

18. 1. (3, 0)
2. (8, 0)
3. (0, -4)
4. (0, -6)

19. 1. (-1, 0)
2. (-8, 0)
3. (0, 2)
4. (0, 4)

20. What is the y-intercept of
x = 3?
1. (3, 0)
2. (-3, 0)
3. (0, 3)
4. None

21. 21
Class Work:
 CW 3.4; Due Today
 CW 3.5; due date is now 02/16/16

22. 22
Finding the x-and y-intercepts of Linear Equations
The path of the defender crosses the path of the thrown football.
In algebra, what are x- and y-intercepts?
What does it mean to INTERCEPT a pass in football?