1. TLW identify linear equations and intercepts.
Linear Functions
TLW identify linear equations and intercepts.

2. A linear equation is the equation of a line.
The standard form of a linear equation is
Ax + By = C
* A has to be positive and cannot be a fraction.

3. Examples of linear equations
2x + 4y =8
6y = 3 – x
x = 1
-2a + b = 5
Equation is in Ax + By =C form
Rewrite with both variables on left side … x + 6y =3
B =0 … x + 0 y =1
Multiply both sides of the equation by -1 … 2a – b = -5
Multiply both sides of the equation by 3 … 4x –y =-21

4. Examples of Nonlinear Equations
The following equations are NOT in the standard form of Ax + By =C:
The exponent is 2
There is a radical in the equation
Variables are multiplied
Variables are divided
4x2 + y = 5
xy + x = 5
s/r + r = 3

5. This IS a linear equation.
Determine whether the equation is a linear equation, if so write it in standard form.
y = 5 – 2x
y = 5 – 2x
Rewrite the equation
+ 2x
+ 2x
Add 2x to each side
2x + y = 5
Simplify
A = 2, B= 1, C=5
This IS a linear equation.

6. Determine whether the equation is a linear equation, if so write it in standard form.
2xy -5y = 6
Since the term 2xy has two variables, the equation cannot be written in the form Ax + By =0. Therefore, this is NOT a linear equation.

7. Determine whether the equation is a linear equation, if so write it in standard form.
Since the term x is raised to the second power, the equation cannot be written in the form Ax + By =0. Therefore, this is NOT a linear equation.

8. This IS a linear equation.
Determine whether the equation is a linear equation, if so write it in standard form.
y = 6 – 3x
Rewrite the equation
y = 6 – 3x
Add 3x to each side
+ 3x
+ 3x
3x +y = 6
Simplify
A = 3, B= 1, C=6
This IS a linear equation.

9. This IS a linear equation.
Determine whether the equation is a linear equation, if so write it in standard form.
Multiply everything by the denominator to get rid of the fraction
(4)
x + 20y = 12
A = 1, B= 20, C=12
This IS a linear equation.

10. Determine whether the equation is a linear equation, if so write it in standard form.
-4x+7=2

11. X and Y intercepts
The x coordinate of the point at which the graph of an equation crosses the x –axis is the x- intercept .
The y coordinate of the point at which the graph of an equation crosses the y-axis is called the y- intercept.
y- intercept
(0, y)
X- intercept
(-x,0)

12. Graph the linear equation using the x- intercept and the y intercept
3x + 2y = 9
To find the x- intercept, let y = 0
Original Equation
3x + 2y = 9
3x + 2(0) = 9
Replace y with 0
3x = 9
Divide each side by 3
x = 3
To find the y- intercept, let x = 0
Original Equation
3x + 2y = 9
3(0) + 2y = 9
Replace x with 0
2y = 9
Divide each side by 2
y = 4.5
Plot the two points and connect them to draw the line.

13. Graph the linear equation using the x- intercept and the y intercept
2x + y = 4
To find the x- intercept, let y = 0
2x + y = 4
Original Equation
2x + (0) = 4
Replace y with 0
Divide each side by 3
2x =4
x = 2
To find the y- intercept, let x = 0
2x + y = 4
Original Equation
2(0) + y = 4
Replace x with 0
Simplify
y = 4
Plot the two points and connect them to draw the line.

14. Identify the x- and y- intercepts given a table-1 -6 -4 1 -2 2 3 X Y -4 1 -3 -2 -1

15. Find the x and y- intercepts of x = 4y – 5
Plug in x = 0
x = 4y - 5
0 = 4y - 5
5 = 4y
= y
(0, ) is the
y-intercept
x-intercept:
Plug in y = 0
x = 4y - 5
x = 4(0) - 5
x = 0 - 5
x = -5
(-5, 0) is the
x-intercept

16. Find the x and y-intercepts of g(x) = -3x – 1*
Plug in x = 0
g(x) = -3(0) - 1
g(x) = 0 - 1
g(x) = -1
(0, -1) is the
x-intercept
Plug in y = 0
g(x) = -3x - 1
0 = -3x - 1
1 = -3x
= x
( , 0) is the
*g(x) is the same as y

17. Find the x and y-intercepts of 6x - 3y =-18
x-intercept
Plug in y = 0
6x - 3y = -18
6x -3(0) = -18
6x - 0 = -18
6x = -18
x = -3
(-3, 0) is the
y-intercept
Plug in x = 0
6x -3y = -18
6(0) -3y = -18
0 - 3y = -18
-3y = -18
y = 6
(0, 6) is the

18. Find the x and y-intercepts of x = 3
A vertical line never crosses the y-axis.
There is no y-intercept.
x-intercept
Plug in y = 0.
There is no y. Why?
x = 3 is a vertical line so x always equals 3.
(3, 0) is the x-intercept. x y

19. Find the x and y-intercepts of y = -2
x-intercept
Plug in y = 0.
y cannot = 0 because
y = -2.
y = -2 is a horizontal
line so it never crosses
the x-axis.
There is no x-intercept.
y-intercept
y = -2 is a horizontal line
so y always equals -2.
(0,-2) is the y-intercept. x y

20. Graph by making a table Graph x y (x, y) -2 -4 (-2, -4) -3 (0, -3) 2
Select values from the domain and make a table. Then graph the order pairs. Draw a line through the points x y
(x, y) -2 -4
(-2, -4) -3
(0, -3) 2 -2
(2, -2)

22. Graph by making a table Graph x y (x, y)
Select values from the domain and make a table. Then graph the order pairs. Draw a line through the points x y
(x, y)

23. Questions??