Today:

Review for Thursday's Test This Week's Khan Academy Topics New Concept: The Slope of a Line

CW 3.5 Questions Answered (Due Tomorrow)

Progress Reports Thursday

February 16, 2016

But first...the final results from the thrilling world of Cricket...

1st Coordinate Plane Test: Thursday, Feb. 18; The Test will include the following:

Functions, Domain, Range Ordered Pair Solutions

Standard Form of a Line/Intercepts Slope of a Line

Grade

Trackers

For today, you need: Grade trackers, Notebook, graph paper,

calculatorWork the problems out. A wrong answer is far better than no answer..

Find Intercepts from a Linear Equation

2/21/16

Topic DueDate

Domain & Range from Graph 2/21/16

Interpreting Graphs of Linear & Non-Linear

Functions

2/21/16

WARM●UP Graph Paper

Out

●

●

Domain & Range from Graph

-3

9-3

6

Is the graph a function?Is the graph a

linear function?

Domain & Range from Graph

-6

6 -8

9

Is the graph a function?

Is the graph a linear function?

Domain & Range from Graph

Is the graph a function?

Is the graph a linear function?

-2

7

0 4

1. The x values in a relation are called the:

2. The range of this relation { (-2,1); (-4,1); (2,5); (-2,3); (4,8); } is: a) {-2,1,2,-2,4} b) {1,3,5,3,8} c) {1,1,5,3,8} d) {-2,1,2,-4,8} e) none3. Given y = -2x – 3, the f (-5) is: 4. What are the x and y intercepts for: 2x – 6 = y

5. Which ordered pair is not a solution to: y = 4x - 10

a) -13 b) 0 c) -3 d) 7 e) none

a) (0,4) b) (3,0) c) (3,-6) d) (-3,6) e) none

5 Question Test Review:

a) (1,-6) b) (0,-10) c) (-1,-6) d) (2,-2) e) none

Number your paper 1-5; do not say the answer out loud...

a) domain b) range c) ordered pair d) output e) none

Graph the equation with at least 3 points: 3y = 2x - 6

Can you simplify an equation, say, 4x - 6y =

12 and still get the same line?

Where/How to Start?- 2x +3y = -6; 2x - 3y = 62x - 3(0) = 6

x = 3

●

2(0) - 3y = 6

y = -2

●

●

Use the slope of the line to find one more point.

What is the y coordinate when x is 150?y =

98

...Find the intercepts

+

+

--

Graph paper out, try to work the problem completely!

y is 4 more than the product of 7 and x; x = 3

Write a function rule that represents each sentence. Then find the value of y for the given value of x.

You got the answer correct. That's good, but what does it mean?What do those two numbers represent?

y is 11 less than of x; x = 72

Write the following function rule in function notation. Again, find the value of

the function at the given x.f(x) = (72) - 11

f(x) = 13

y = 7(3) + 4; y = 25

Warm-Up

Find any other point on this same line.

2. Find the range values of the function for the given domain.

f(x) = -3x + 2 ; {-5, -2, 6}Steps1. Sub in each domain value one @

a time.2. Solve for y in each equation3. List y values in braces.The range values of the function f(x) = -2x + 3,

with a domain of {-5, -2, 6} are..... {17, 8, -16}

Test Review

What are three of the coordinates of this line? (-5, 17), (-2, 8),

(6, -16)

Test Review

Test Review

From the graph below, which equation contains point B?

Test Review

Class Notes Section of Notebook

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

What is the equation of this line?

The point here,

is called the....y-intercept. We know the

slope, and the y-intercept, so...

y = x - 2

What is the slope of this line?

The Slope of a Line