1. Warm-up:
Given: point A: (1, 2) point B: (x, 6) The distance between point A and point B is 5. Use the distance formula to find x.

2. HW Answers pg.65 (30), pg. 65(32-40 even) b and c only
4, 7,
13, (7/2, 6)
34) 15, (-5/2, 2)
, (6, 6)
, (-1/4, -5/12)
40) , (-5.6, 8.6)

3. Objective:
review graphing linear equations.
graph quadratic equations

4. What is a Linear Equation?
A linear equation is an equation whose graph forms a straight line.
Linear equations are usually shown on a Cartesian coordinate plane
Real life situations of linear equations include the stock market as well as the payments of a car.

5. Parts of a Coordinate Plane
QUADRANT II
(-x, y)
QUADRANT I
(x, y)
Origin
QUADRANT III
(-x, -y)
QUADRANT IV
(x, -y)
X-Axis
Y-Axis

6. Slope
Slope is the ratio of vertical change to the horizontal change (rise/run) of a line.
Slope in a linear equation shows if the line is ascending (positive) or descending (negative).
Slope can also show the rate of change.
The letter m is used to represent slope in a formula.

7. Forms of Linear Equations
The forms of linear equations are the formats in which the information is written.
These two forms are the most commonly used ways to write linear equations.
1. Slope Intercept Form: y = mx + b
2. Standard Form: Ax + By = C

8. Slope Intercept Form * ¾ is the slope.
Slope intercept form is y = mx + b.
This form makes it easy to find the slope (m) and the y-intercept (b).
Working with this form is simple, so it is used more often than other forms.
Example:
* ¾ is the slope.
* 3 is the point where the line crosses the Y-axis.

9. Graph Using Slope Intercept Form
1) Graph the y-intercept b = -1.
2) From the y-intercept point, use the slope m = ½ to rise one and run two in order to find a second point
3) Plot as many points as desired using the slope, then draw a line through the points.
Run 2
Rise 1

10. Standard Form Ax + By = C Example: 3x + 2y = 6
It can be used to find the x and y-intercept points of the equation.
Example: 3x + 2y = 6
1) Substitute in a zero for x. Simplify.
3(0) + 2y = 6
y = 3
2) One point of the line is (0, 3). Plot the point.
3) Substitute y with zero. Simplify.
3x + 2(0) = 6
x = 2
4) The second point is (2, 0). Plot it and draw a line through the two points.

11. Steps to graph quadratic equations:
y = ax2 + bx + c
1. Put the equation in standard form:
2. Identify the values of a, b, and c.
3. Find the axis of symmetry:
(vertical line)

12. 4. Find your vertex (substitute your axis of symmetry
back into the original equation and solve for y).
Construct a table of values for x and y.
Choose values of x, two above and two below
your x value in the vertex.
Plot the points and connect them with a U-shaped curve.

13. Graph opens up or opens down?
If a is positive, then the
parabola will open up.
If a is negative, then the
parabola will open down.

14. OPENS DOWN
a = -1
b = 2
c = -1 x
-(x)2+2x-1 y
(x, y) 

15. a = 1
b = -6
c = 5
OPENS UP x
x2- 6x + 5 y
(x, y) 

16. OPENS DOWN
a = -1
b = -2
c = 3 x
-(x)2- 2x+3 y
(x, y) 

17. Sneedlegrit:
OPENS DOWN
a = 1
b = 2
c = -6 x
(x)2 +2x-6 y
(x, y) 

18. Homework: worksheet