Slope, using proportions, and rate of change Mr. Smith.
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Transcript of Slope, using proportions, and rate of change Mr. Smith.
![Page 1: Slope, using proportions, and rate of change Mr. Smith.](https://reader036.fdocuments.in/reader036/viewer/2022070415/5697bfa91a28abf838c99f30/html5/thumbnails/1.jpg)
Slope, using proportions, and rate of change
Mr. Smith
![Page 2: Slope, using proportions, and rate of change Mr. Smith.](https://reader036.fdocuments.in/reader036/viewer/2022070415/5697bfa91a28abf838c99f30/html5/thumbnails/2.jpg)
Use given information to find the rate of change
Went from 11.3 to 12.4 from 1990 to 1994
Solve for the missing coordinate when given the slopem=, (5,r) (2, -3) m=, (r, 5) (-2, r)
Find the slope of a line given 2 points(2, -1) (5, -3) (2), (-, )
BY THE END OF THIS SLOPE LESSON YOU SHOULD BE ABLE TO SOLVE THE FOLLOWING LEVELS OF PROBLEMS THAT YOU WILL BE ASSESSED
ON:
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What is slope?
• Slope is the Steepness of a line. In this section it can be found by using 2 given points that lie on the line.
• Slope can be positive, negative, zero (y value repeats, horizontal), or undefined (x value repeats, vertical)
• The steeper the slope, whether positive or negative, the greater the slope.
• Slope is constant, it is always the same, like a rate of change (miles per hour or millions per year).
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m =
• Slope is the change in y divided by the change in x.
• Find the slope with the following 2 points:• (-3, 6) (5, 9)
• m = =
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m =
1. (2, -1), (5, -3) 2. (2), (-, )
Pause and try
![Page 7: Slope, using proportions, and rate of change Mr. Smith.](https://reader036.fdocuments.in/reader036/viewer/2022070415/5697bfa91a28abf838c99f30/html5/thumbnails/7.jpg)
m =
1. (2, -1), (5, -3)
m = =
2. (2), (-, )
m = =
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Finding the missing values when given slope
• Use proportions to find missing values
• Use distributive property to make an equation that uses 2 or 3 steps to solve
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You can use cross products to solve for a missing coordinate
m = , (r, 6) (10, -3)
-30 +3r = -18+30 +30 3r = 12 3 3 r = 4
m= , (4, r) (r, 2)
= -5r + 20 = 6 – 3r+5r + 5r 20 = 6 +2r -6 = -6 14 = 2r 2 2 7 = r
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Solve for r
m=, (5,r) (2, -3) m=, (r, 5) (-2, r)
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Solve for r
m=, (5,r) (2, -3)
=
= -12 = -9-3r +9 +9-3 = -3r -3 -3
1 = r
m=, (r, 5) (-2, r)=4 + 2r = 9r - 45 +45 +4549 + 2r = 9r - 2r -2r49 = 7r 7 77 = r
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Find the rate of change
• Use the given information as points. Units (years, minutes, etc.) are the x, and the totals are the y.
• The rate of change is also the slope.
• When karen was 12 years old, she was 60 inches high. When she was 18, she was 67 inches high. Find the rate of change.
(12, 60) , (18, 67)
= = = 1 in. is the rate
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Find the rate of change
• From 1990 to 1994 public school enrollment went from 11.3 to 12.5 million students. What was the rate of change?
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Find the rate of change
• From 1990 to 1994 public school enrollment went from 11.3 to 12.5 million students. What was the rate of change?
(1990, 11.3) (1994, 12.5)= = .3