Warm - Up; Khan Topic Continue Slope Practice

Slope - Intercept Formula

Interpreting Graphs of Linear

and Non-Linear Functions

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nonlinear

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Linear/ Nonlinear

Given this,

what are the x and y axes?

faster 1

67twice

• Find the range of the function below when the domain is {-4, -1, 3} y = |x| - 2

Warm Up/Test Review

4 0 0 -13

The Slope of a Li

ne

x

y

x2 – x1

y2 – y1

change

in ychange in x

The slope of the line passing through the two points (x1, y1) and (x2, y2) is given by the formula

(x1, y1)

(x2, y2)

y2 – y1

x2 – x1

m = , (x1 ≠ x2 ).

The rise is the difference of the y-values of two points on a line.The run is the difference in the x-values of two points on a line.

The constant rate of change of a straight line is called the slope.

The Slope of a Line:

Slope is usually represented by the letter m (from the French, monter, which

means “to go up”).

Straight Lines (linear functions) are straight because the slope never changes!!

(3, 2)

(–1, –2)

Then count horizontally to a second point to find the run.

Count vertically from any one point on the line to find the rise.

Finding the Slope of a Line

slope = = 1

The slope of the line is 1.

It does not matter which ordered pair you start with.

slope = = 1

44

(5, 4)

Then count horizontally to a second point to find the run.

Count vertically from any one point on the line to find

the rise.

slope = =

The slope of the line is

slope = =

Find the slope of the line:

It does not matter which y you begin from.

(1, 2)

The Slope of a Line

The slope of a line is the ratio of rise to run for any two points on the line.change in y

change in x Rise Run=

Find the slope of the line passing through the points (2, 3) & (4, 5).

The x1 and y1 must come from the same ordered pair.

y2 – y1

x2 – x1

m = 5 – 3 4 – 2

= = 22

= 1

2

2(2, 3)

(4, 5)

x

y

The Slope of a Line

Name one other ordered pair on this

line.

The Slope of a LineWhat is the slope of this, and all horizontal lines?Don't guess,

just plug the numbers in...

All horizontal lines have a slope of zero.

The Slope of a LineWhat is the slope of this, and all vertical lines?

All vertical lines have a slope that is undefined because... a

denominator cannot be zero.

y

x2-2

The slope of a line is a number, m, which measures its steepness.

m = 0

m = 2

m is undefined

m =12

m = - 14

The slope of a line reveals how the f(x) is affected by a change in x

What does a steeper line tell you about the y

variable?

y2 – y1

x2 – x1m =

The Slope of a Line

The Slope of a Line

What is the slope of the line?

The Slope of a Line

Find the next point in both directions

Find the slope of each line:

23

m =

m = m = -

1

Grand Prix Go-Carts:

What is the y-intercept?

What are the independent (x) and dependent (y)

variables?How does each change in the x variable affect the dependent, y variable? In other words, what is the rate of change?Which graph shows the price function?

Test Review:

A

BC

D E

Is this graph a function?By what percent did the price of silver

drop between Aug. 7th & August 9th?36%

Test Review: