FindingSlope.ppt
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This document provides instruction on calculating and understanding slope. It defines slope as the steepness of a line and discusses how to calculate slope given two points on a line using the rise over run formula or the slope formula. It provides examples of finding the slope of lines from their graphs or given two points and discusses the slopes of horizontal and vertical lines.
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This document provides an overview of linear equations and graphing lines. It covers basic coordinate plane information, plotting points, finding slopes, x- and y-intercepts, the slope-intercept form of a line, graphing lines using tables and slope-intercept form, and determining the equation of a line given different information like two points or a slope and point. The assignments section indicates students will apply these concepts to practice problems.1555 linear equations
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The document provides information about calculating the slope of a line from a graph or two points, including examples and practice problems. Key terms are defined, such as rise, run, slope, dependent and independent variables. An example problem demonstrates how to find the slope from a table of gas costs and gallons and interpret what the slope represents. A lesson quiz provides practice finding slopes and interpreting what they represent based on graphs and tables.
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The document discusses various formulas used to represent lines in the coordinate plane, including:
- Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
- Point-slope form: y y1 = m(x x1), where (x1, y1) is a known point on the line and m is the slope.
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3-7
Objective To graph and write linear equations
Ski resorts often use steepness to rate the difficulty
of their hills. The steeper the hill, the higher the
difficulty rating. Below are sketches of three new hills
at a particular resort. Use each rating level only once.
Which hill gets which rating? Explain.
Difficulty Ratings
Easiest
Intermediate
Difficult
3300 ft 3000 ft 3500 ft
1190 ft 1180 ft 1150 ft
A B C
Th e Solve It involves using vertical and horizontal distances to determine steepness.
Th e steepest hill has the greatest slope. In this lesson you will explore the concept of
slope and how it relates to both the graph and the equation of a line.
Essential Understanding You can graph a line and write its equation when you
know certain facts about the line, such as its slope and a point on the line.
Equations of Lines in the
Coordinate Plane
Think back!
What did you
learn in algebra
that relates to
steepness?
Key Concept Slope
Defi nition
Th e slope m of a line is the
ratio of the vertical change
(rise) to the horizontal change
(run) between any two points.
Symbols
A line contains the
points (x1, y1) and
(x2, y2) .
m 5
rise
run 5
y2 2 y1
x2 2 x1
Diagram
(x2, y2)
(x1, y1)
O
x
y run
rise
Lesson
Vocabulary
slope
slope-intercept
form
point-slope form
L
V
L
V
s
LL
VVV
s
hsm11gmse_NA_0307.indd 189 2/24/09 6:49:09 AM
http://media.pearsoncmg.com/aw/aw_mml_shared_1/copyright.html
Problem 1
Got It?
190 Chapter 3 Parallel and Perpendicular Lines
Finding Slopes of Lines
A What is the slope of line b?
m 5
2 2 (22)
21 2 4
5 4
25
5 245
B What is the slope of line d?
m 5
0 2 (22)
4 2 4
5 20 Undefi ned
1. Use the graph in Problem 1.
a. What is the slope of line a?
b. What is the slope of line c?
As you saw in Problem 1 and Got It 1 the slope of a line can be positive, negative,
zero, or undefi ned. Th e sign of the slope tells you whether the line rises or falls
to the right. A slope of zero tells you that the line is horizontal. An undefi ned slope
tells you that the line is vertical.
You can graph a line when you know its equation. Th e equation of a line has diff erent
forms. Two forms are shown below. Recall that the y-intercept of a line is the
y-coordinate of the point where the line crosses the y-axis.
O
y
c
b
d a
x
2
2 86
4
6
( 1, 2)
(4, 2)
(4, 0)
(5, 7)(1, 7)
(2, 3)
Positive slope
O
x
y
Negative slope
O
x
y
Zero slope
O
x
y
Undefined slope
O
x
y
Key Concept Forms of Linear Equations
Defi nition
Th e slope-intercept form of an equation of
a nonvertical line is y 5 mx 1 b, where m
is the slope and b is the y-intercept.
Symbols
Th e point-slope form of an equation of a
nonvertical line is y 2 y1 5 m(x 2 x1),
where m is the slope and (x1, y1) is a point
on the line.
y mx b
slope y-intercept
y y1 m(x x1)
slope x-coordinatey-coordinate
A
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The document discusses various formulas used to represent lines in the coordinate plane, including:
- Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
- Point-slope form: y y1 = m(x x1), where (x1, y1) is a known point on the line and m is the slope.
- Standard form: Ax + By = C, where A, B, and C are constants and A and B cannot both be 0.
It provides examples of writing equations of lines in different forms given information like the slope, a point, or the graph of the line. Converting betweenWRITING AND GRAPHING LINEAR EQUATIONS 1.pptx
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The document discusses linear equations and graphing lines. It covers plotting points, calculating slope, writing equations in slope-intercept form, and graphing lines by making a table or using the slope and y-intercept. Methods are presented for finding the equation of a line given two points, the slope and a point, or from a graph.Lesson 3-7 Equations of Lines in the Coordinate Plane 189.docx
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Ski resorts often use steepness to rate the difficulty
of their hills. The steeper the hill, the higher the
difficulty rating. Below are sketches of three new hills
at a particular resort. Use each rating level only once.
Which hill gets which rating? Explain.
Difficulty Ratings
Easiest
Intermediate
Difficult
3300 ft 3000 ft 3500 ft
1190 ft 1180 ft 1150 ft
A B C
Th e Solve It involves using vertical and horizontal distances to determine steepness.
Th e steepest hill has the greatest slope. In this lesson you will explore the concept of
slope and how it relates to both the graph and the equation of a line.
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know certain facts about the line, such as its slope and a point on the line.
Equations of Lines in the
Coordinate Plane
Think back!
What did you
learn in algebra
that relates to
steepness?
Key Concept Slope
Defi nition
Th e slope m of a line is the
ratio of the vertical change
(rise) to the horizontal change
(run) between any two points.
Symbols
A line contains the
points (x1, y1) and
(x2, y2) .
m 5
rise
run 5
y2 2 y1
x2 2 x1
Diagram
(x2, y2)
(x1, y1)
O
x
y run
rise
Lesson
Vocabulary
slope
slope-intercept
form
point-slope form
L
V
L
V
s
LL
VVV
s
hsm11gmse_NA_0307.indd 189 2/24/09 6:49:09 AM
http://media.pearsoncmg.com/aw/aw_mml_shared_1/copyright.html
Problem 1
Got It?
190 Chapter 3 Parallel and Perpendicular Lines
Finding Slopes of Lines
A What is the slope of line b?
m 5
2 2 (22)
21 2 4
5 4
25
5 245
B What is the slope of line d?
m 5
0 2 (22)
4 2 4
5 20 Undefi ned
1. Use the graph in Problem 1.
a. What is the slope of line a?
b. What is the slope of line c?
As you saw in Problem 1 and Got It 1 the slope of a line can be positive, negative,
zero, or undefi ned. Th e sign of the slope tells you whether the line rises or falls
to the right. A slope of zero tells you that the line is horizontal. An undefi ned slope
tells you that the line is vertical.
You can graph a line when you know its equation. Th e equation of a line has diff erent
forms. Two forms are shown below. Recall that the y-intercept of a line is the
y-coordinate of the point where the line crosses the y-axis.
O
y
c
b
d a
x
2
2 86
4
6
( 1, 2)
(4, 2)
(4, 0)
(5, 7)(1, 7)
(2, 3)
Positive slope
O
x
y
Negative slope
O
x
y
Zero slope
O
x
y
Undefined slope
O
x
y
Key Concept Forms of Linear Equations
Defi nition
Th e slope-intercept form of an equation of
a nonvertical line is y 5 mx 1 b, where m
is the slope and b is the y-intercept.
Symbols
Th e point-slope form of an equation of a
nonvertical line is y 2 y1 5 m(x 2 x1),
where m is the slope and (x1, y1) is a point
on the line.
y mx b
slope y-intercept
y y1 m(x x1)
slope x-coordinatey-coordinate
A
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MAT1033.4.1.pptElmabethDelaCruz1
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098A_exponents_factoring.pptElmabethDelaCruz1
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3-Special Factoring.pptElmabethDelaCruz1
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FindingSlope.ppt
- 1. Objective The student will be able to: find the slope of a line given 2 points and a graph. SOL: A.6a Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS
- 2. What is the meaning of this sign? 1. Icy Road Ahead 2. Steep Road Ahead 3. Curvy Road Ahead 4. Trucks Entering Highway Ahead
- 3. What does the 7% mean? 7% is the slope of the road. It means the road drops 7 feet vertically for every 100 feet horizontally. 7% So, what is slope??? Slope is the steepness of a line. 7 feet 100 feet
- 4. Slope can be expressed different ways: A line has a positive slope if it is going uphill from left to right. A line has a negative slope if it is going downhill from left to right. 2 1 2 1 ( ) vertical change ( ) horizontal change y y rise m x x run
- 5. When given the graph, it is easier to apply rise over run. 1) Determine the slope of the line.
- 6. Start with the lower point and count how much you rise and run to get to the other point! Determine the slope of the line. 6 3 run 3 6 = = 1 2 rise Notice the slope is positive AND the line increases!
- 7. 2) Find the slope of the line that passes through the points (-2, -2) and (4, 1). (1 ( 2)) (4 ( 2)) m 2 1 2 1 ( ) ( ) y y m x x (1 2) (4 2) When given points, it is easier to use the formula! y2 is the y coordinate of the 2nd ordered pair (y2 = 1) y1 is the y coordinate of the 1st ordered pair (y1 = -2) 1 3 6 2
- 8. Did you notice that Example #1 and Example #2 were the same problem written differently? (-2, -2) and (4, 1) 6 3 1 2 slope You can do the problems either way! Which one do you think is easiest?
- 9. Find the slope of the line that passes through (3, 5) and (-1, 4). 1. 4 2. -4 3. 村 4. - 村
- 10. 3) Find the slope of the line that goes through the points (-5, 3) and (2, 1). m y2 y1 x2 x1 1 3 2 ( 5) m 1 3 2 5 m 2 7 m
- 11. Determine the slope of the line shown. 1. -2 2. -遜 3. 遜 4. 2
- 12. Determine the slope of the line. The line is decreasing (slope is negative). 2 -1 rise run 2 1 2 Find points on the graph. Use two of them and apply rise over run.
- 13. What is the slope of a horizontal line? The line doesnt rise! m 0 number 0 All horizontal lines have a slope of 0.
- 14. What is the slope of a vertical line? The line doesnt run! All vertical lines have an undefined slope. m number 0 undefined
- 15. Remember the word VUXHOY Vertical lines Undefined slope X = number; This is the equation of the line. Horizontal lines O - zero is the slope Y = number; This is the equation of the line.
- 16. 1 Draw a line through the point (2,0) that has a slope of 3. 1. Graph the ordered pair (2, 0). 2. From (2, 0), apply rise over run (write 3 as a fraction). 3. Plot a point at this location. 4. Draw a straight line through the points. 3
- 17. The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r. To solve this, plug the given information into the formula m (y2 y1 ) (x2 x1 ) . 2 6 4 4 r
- 18. 4 4 1 4 r To solve for r, simplify and write as a proportion. 4 4 1 4 r 2 6 4 4 r Cross multiply. 1(-4) = 4(4 r)
- 19. Simplify and solve the equation. 1(-4) = 4(4 r) -4 = 16 4r -16 -16 -20 = -4r -4 -4 5 = r The ordered pairs are (5, 6) and (4, 2)