1. Section 2-2 : Linear Equations
Linear equations graph as lines.
Standard form: Ax + By = C, where A, B, & C are real numbers. (A & B cannot both be 0).
The key to standard form is that both variables are on the same side.

2. Linear Equations The variables do not have exponents.
The variables are not being multiplied by each other.
No radicals (square roots).

3. Linear Equations Linear 6y = 3 - x x = 1 -2a + b = 5 4x - y = -7 3
Not Linear
4x2 + y = 5
x =
xy + x = 5
s/r + r = 3

4. Linear Equations
Linear Functions: linear equations that are functions (no value of the domain is repeated).
Usually in the form f(x) = mx + b. (hopefully you remember y =mx+b which is slope-intercept form of an equation. m = slope, b = y-int.)

5. Finding x and y intercepts
x-intercept - the point where a line crosses the x-axis.
What is the y-coordinate of that point?
The general form of the x-int. is (x, 0). The y-coor. will always be zero.

6. Finding x and y intercepts
y-intercept - the point where a line crosses the y-axis.
What is the x-coordinate of that point?
The general form of the y-int. is (0, y). The x-coor. will always be zero.

7. Finding x and y intercepts
If we have the equation 2x + y = 6, and we know that y = 0, what must x be?
Plug in 0 for y and simplify.
2x + 0 = 6 => 2x = 6 => x = 3
So (3, 0) is a point on the line.

8. Finding x and y intercepts
What we just found was the x-intercept of the line with the equation 2x + y = 6.
How do we know? They y coor. was equal to 0. So it has to be on the x-axis!!

9. Finding x and y intercepts
To find the x-intercept, plug in 0 for y.
To find the y-intercept, plug in 0 for x.

10. Find the x and y intercept x = 4y - 5
x-intercept:
Plug in y = 0
x = 4(0) - 5
x = 0 - 5
x = -5
(-5, 0) is the x-int.
y-intercept:
Plug in x = 0
0 = 4y - 5
5 = 4y
5/4 = y
(0, 5/4) is the y-int.

11. Find the x and y intercepts g(x) = -3x - 1
x-intercept
g(x) = -3x - 1 is y = -3x - 1
plug in 0 for y
0 = -3x - 1
1 = -3x, -1/3 = x
(-1/3, 0)
y-intercept
y = -3(0) - 1
y = 0 - 1
y = -1
(0, -1)

12. find the x and y intercepts 6x - 3y =-18
x-intercept
6x - 3(0) = -18
6x - 0 = -18
6x = -18
x = -3
(-3, 0)
y-intercept
6(0) - 3y = -18
0 - 3y = -18
-3y = -18
y = 6
(0, 6)

13. Find the x and y intercepts x = 9
x-intercept
plug in 0 for y? There is no y, why?
It is a vertical line, x always equals 9. (9, 0) is x-intercept.
This vertical line never crosses the y-axis, thus no y-intercept.

14. Graphing Equations Graph the equation -5x + y = 2.
Use the graphing calculator.
Solve for y first.
Add 5x to both sides.
y = 5x + 2

15. Graph -5x + y = 2 From main menu, go to table. (7) Type in 5x + 2
Hit EXE then F6.
You should come up with a table of values. Choose 3 ordered pairs.
Graph them & connect.

16. Graph -5x + y = 2 x y

17. Graph 4x - 3y = 12 Solve for y. Subtract 4x from both sides.
-3y = -4x Divide by -3.
y = -4x/ /-3. Simplify.
y = x - 4

18. Graph 4x - 3y = 12
From the table menu, delete any equations and plug in x - 4.
Show the table and choose three points. Graph them and connect. x y

19. Wkst 2.2 (from share folder)
Assignment: Section 2-2
Wkst 2.2
(from share folder)