1. Chapter 8 : Analytic Geometry
By Andrei and Rashad

2. Introduction Lengths of a line segment are always positive (+)
Some examples of surfaces that slope are mountain, wheelchair ramp, and house roofs
Lengths of a line segment are always positive (+)
19cm Line Segment

3. Slope The slope of a line measures how steep it is
In this graph, you can see that line 2 is steeper than line 1
If the line falls from left to right, they have negative slopes (as shown in the example)
If the line rises from left to right, it has a positive slope

4. Calculating Slope Slope (m) = rise (change in y) / run (change in x)
Rise is the vertical change and run is the horizontal change
M = y/x
M = 3/3
M = 1
The slope is 1. This means that for every increase of 1 on the x axis, there will be an increase of 1 on the y axis.
Rise (3)
Run (3)

5. Calculating Slope Another formula to calculate slope is m = Dy / Dx
Dy means (y2 – y1)
Dx means (x2 – x1)
Lines with positive slopes have positive numerical slopes
Lines with negative slopes have negative numerical slopes

6. Horizontal and Vertical Lines
Horizontal lines have a slope of 0
Vertical lines have a slope that is undefined
UNDEFINED

7. Point-Slope and Standard Form
There are 2 ways to find the equation of a line
One is the standard form, which is ‘Ax + By + C = 0
A, B, and C can equal any real number. X is the x-intercept and Y is the y-intercept.
The other form is ‘y-y1 = m(x-x1)’
Plug in the coordinates of the first point for x1 and y1

8. X- and Y- Intercepts
Y-intercept is the point where the line crosses the y-axis
X-intercept is the point where the line crosses the x-axis

9. Slope and Y-Intercept Form
A third way to find the equation of a line is slope and y-intercept form
The equation is ‘Y= mx + b’

10. Methods for Graphing Linear Equations
You can use a table of values. For example, if the equation is: y=1/2x+1, the table would look like:
Then, you just plot the points on the
Cartesian Plane, for example, the
first point would be (0,1) and then
(2,2) and (4,3) x
1/2x+1 y
1/2(0)+1 1 2
1/2(2)+1 4 3

11. Parallel and Perpendicular Lines
If 2 lines are parallel, they will have the same slope (m1 = m2)
All vertical lines are parallel
If 2 lines are parallel, their slopes multiplied by each other will equal -1 (this is called a negative reciprocal)

12. Intersecting Lines
A point of intersection is the point where the lines meet