Upcoming SlideShare
×

# Slope and Equations of Lines

2,300 views

Published on

Published in: Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
2,300
On SlideShare
0
From Embeds
0
Number of Embeds
201
Actions
Shares
0
70
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Slope and Equations of Lines

1. 1. SLOPES AND EQUATIONS OF LINES
2. 2. SLOPE Slope is the rate of change of a straight line (linear) graph/function.  What are some of the things we have learned about slope so far?  Can you come up with an equation to calculate slope? Image From: http://www.mathwarehouse.com/algebra/linear_equation/slope-of-a-
3. 3. SLOPE CONT.  Positive slopes mean the graph is going up from left to right  Negative slopes mean the graph is going down from left to right  The steeper the line the bigger the slope (rate of change) Image From: http://www.sparknotes.com/math/algebra1/writingequations/section1.rhtml Image From:
4. 4. HOW TO CALCULATE SLOPE… To calculate a slope from a graph or two coordinate points we use the formula: Image From: http://math.about.com/od/allaboutslope/ss/Find-Slope-With-Formula-
5. 5. FINDING SLOPE • Use the slope formula to find the slope of the given examples. 1. (-2, 5) and (4, 12) 2. Image From: https://www.mathscore.com/math/skills/DetSlope.html
6. 6. SLOPE VIDEOS Graphical Example for Slope of a Line Example of Finding Slope given Two Points Video From: Khan Academy
7. 7. LINEAR FUNCTIONS Linear Functions are functions whose graphs are straight lines. They are straight because their rate (slope) is constant. There are 3 forms of a linear function. • Slope-Intercept Form • Standard Form • Point-Slope Form
8. 8. SLOPE-INTERCEPT FORM  It is slope-intercept form because the y (or dependent variable) is by itself and the highest exponent of x (or independent variable) is 1.  The slope is always the value with the x in THIS FORM. It could be written y = b + mx. Image From: http://bronxarena.org/mobile/courses/algebrab/challenge1/1.5.html
9. 9. EXAMPLES Write the equation of the line in slope-intercept form. 1. 2. 3. m= 1/5 b = -2 4. y-intercept = 200 slope = -23.724 Image From: http://hotmath.com/help/gt/genericalg1/section_9_2.html Image From: http://www.mathsteacher.com.au/year8/ch15_graphs/04_plot/graphs.htm
10. 10. SPECIAL CASES  Horizontal Lines have a slope of 0. Therefore, we cannot write a slope-intercept equation for them. Horizontal lines intersect the y-axis. Therefore, the equation for a horizontal line just states what that y-value is.  Vertical lines have an undefined slope. Therefore, we cannot write a slope-intercept equation for them, either. • Instead, we notice that the coordinate points of a vertical all have the same x-value. • So, the equation for a vertical line just states what that x-value is.
11. 11. SLOPE-INTERCEPT VIDEO Slope-Intercept Equation Video From: Khan Academy
12. 12. LINEAR STANDARD FORM This is another form for writing a linear function. It is used to represent situations where two variables are changing at a constant rate. In this form, the A, B, and C do not represent the y-intercept or the slope of the graph. It is also important to understand that in many cases standard form is only written using integers (+/- whole numbers) for A, B, and C. It is possible for A, B, and C to be zero but it cannot be both A and B.
13. 13. WHICH EQUATIONS ARE IN LINEAR STANDARD FORM? Linear Standard Form -2x – 4y = 9 X=2 Y=1 Not Linear Standard Form 1/3x – 7y = 12 y = -1/2x + 3 y – 4 = 2(x + 5) 8 = 2.5x – 3y 10 = -3xy 4x + 3y = 20
14. 14. STANDARD FORM VIDEOS Standard Form Equations Video From: Khan Academy
15. 15. POINT-SLOPE FORM • We use point-slope form when we have a point and a slope of a line Image From:
16. 16. POINT-SLOPE VIDEO Ideas Behind Point-Slope Form Point-Slope Form Examples
17. 17. WRITE A POINT-SLOPE EQUATION 1. (2, 5) and m = ½ 1. (-8, 12) and slope = -3 1. (-6, 0) and m = 8 1. Point: (-1, -6) and Point: (-3, 4) 5.