Slope, using proportions, and rate of change

Mr. Smith

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:

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).

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 = =

m =

1. (2, -1), (5, -3) 2. (2), (-, )

Pause and try

m =

1. (2, -1), (5, -3)

m = =

2. (2), (-, )

m = =

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

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

Solve for r

m=, (5,r) (2, -3) m=, (r, 5) (-2, r)

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

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

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?

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