1. Coordinate Geometry & Algebra Review

2. Various Formulas of a Line

3. Graphing Ordered Pairs
Move to the right three, and down four.
First number:
Move either left or right.
Right= positive, Left= negative
Second Number:
Move either up or down
Up= positive, Down = negative

4. Let’s Practice… Graph: (-2, 5) Graph: (4, -2) Graph: (1, 3)

5. What is Slope?
Slope: describes the steepness or incline of a line. A higher slope value indicates a steeper incline.
Slopes can be positive, negative, zero or undefined.
Slope is abbreviated with “m”

6. Determining Slope Graphically
We can count the rise and run on a graph to determine slope.

7. Finding the Slope Algebraically

8. Let’s Practice…. (3, 5), (2, 4) (4, 1), (3, 7) (-3, 1), (-2, 5)
(8, 4), (6, -5)

9. Finding the Equation of a Line

10. Finding the Equation of a Line
Which formula you chose, depends on the information provided.
You will use both formulas to find slope.

11. Point-Slope Form For example:
Find the equation for a line with points (3, 2) and a slope of -4.

12. Let’s Practice… Find the equation of the line…
Slope = 2, passing through (3, 5)
Slope = 4, passing through (1, 3)
Passing through (1, 2) and ( 5, 10)
Passing through (3, 5) and (8, 15)
Hint: Find the slope 1st for number 3 and 4.

13. What is the y-intercept?
The y-intercept of a line is the point at which the line crosses the y axis. It is where the x value equals 0.
y-intercept = ( 0, y )

14. Slope-Intercept From
For example:
What is the equation of line with a slope of 3 and y-intercept of 6?

15. Let’s Practice…. Find the equation of the line:
slope= 5, y-intercept = -7
slope= 2, y-intercept = -1
slope= 3, y-intercept = 2

16. Parallel Lines Parallel lines have the same slopes.
Are these lines parallel?
1. y = 3x + 10, y = 3x -7
2. y = 1/2x + 2, y = - 1/2x + 4
3. y = 3x + 1, y = 5x +1

17. Writing Equations of Lines Parallel to Given Lines
Write an equation of the lines passing through (-3, 1) and parallel to the line whose equation is y = 2x +1.
What formula are you going to use?
Point-Slope!
Solution: y = 2x + 7

18. Let’s Practice…
Write an equation of the lines passing through (-8, 10) and parallel to the line whose equation is y = -4x + 3.
Solution: y= -4x - 42
2. Write an equation of the lines passing through (-2, -7) and parallel to the line whose equation is y = -5x + 4.
Solution: y= = -5x - 17

19. Perpendicular Lines
Perpendicular Lines have slopes are the negative reciprocal.
For example:
3 and -1/3
-7 and 1/7
½ and -2
-3/4 and 4/3

20. Let’s Practice…
Given the equation of the line in slope-intercept form, what is the slope of a line perpendicular to the given line?
y = 4/3x + 10
y = -7x + 2
y = 1/2x -3
y = -1/3x + 1

21. Let’s Practice…
Given the equation of the line in slope-intercept form, what is the slope of a line perpendicular to the given line?
1. y = 4/3x Perp. Slope = -3/4
2. y = -7x + 2 Perp. Slope = 1/7
3. y = 1/2x -3 Perp. Slope = -2/1 or -2
4. y = -1/3x + 1 Perp. Slope = 3 or 3/1

22. Let’s Practice… Parallel
One line passes through the points (–1, –2) and (1, 2); another line passes through the points (–2, 0) and (0, 4). Are these lines parallel, perpendicular, or neither?
Parallel

23. Let’s Practice…
One line passes through the points (0, –4) and (–1, –7); another line passes through the points (3, 0) and (–3, 2). Are these lines parallel, perpendicular, or neither?
Perpendicular