Today… New Khan Academy Topics

Warm-Up/Final Exam Prep

Using the Coordinate

Formulas

Class Work from Last Week

Class Work

Khan Academy:

Domain & Range from Graph

Domain & Range from Graph

5

1. What is the percent change in the price of gas from $4.80/gal to

$5.00/gal.2. Write the following ratio in

its simplest terms: 3 feet: 4

inches

Warm-Up/Final Exam Review

Take out graph paper and use for all questions that you are asked to graph

3. Simplify: -3(5x - 3) -2(6x - 6)

4. x + 3 = x - 2

6 4

5. x + 2 + x - 1 3 2

= 2

2. From the table, determine the function, fill in the missing values, and write the equation solving for y. f(x) =

Practice Questions:1. From the table, determine the function, fill in the

missing values, and write the equation solving for y. f(x) =

Hint: An easy way to solve all problems of this type is to find the slope, then choose one point and use point-slope to find the slope-intercept form, which is the solution.

Unless....

y = x + 1

y = 2x + 1

Practice Questions:1. The x values in a relation are the:

a.) domain b.) range c.) ordered pair d.) output e.) noneThe 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.) noneGiven y = -2x – 3, the f(-5) is: What are the x and y intercepts for: 2x – 6 = y

Which ordered pair is not a solution to: y = 4x – 10a.) (2,-2) b.) (0,-10) c.) (-1,-6) d.) (1,-6) e.) none

a.) 5 b.) 0 c.) -3 d.) 3 e.) none

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

Practice Questions:The graph shows a soccer player standing,

walking, and running. Match the color with the activity

WalkingStandingRunning

Describe the Slope

Describe the Slope

Practice Questions: What is the

slope of the line?

-

Practice Questions: What is the

slope of the line?-

Practice Questions:

(5, 4)

(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.

Find the Slope of a Line

slope = =24

12

The slope of the line is

12

–2–4

slope = =12

Pick out any two points on the line

Practice Questions:Your double agent is lost in the woods. You have

located her on the grid at (-2,-3). The enemy is close, and the only two safe houses are located closest to this point in the direction of a -2/3 slope from her location. Help your agent escape death by sending her the coordinates of the two safe houses.

Practice Questions:3. The table shows how much money Susan

earned as a house painter for one afternoon. Use the data to make a graph. Find the slope of the line and explain what it shows.

x

y

642 8 10 12 140

1020

30

4050

60

7080

The slope of the line is 7. This means Susan earned $7 for each hour worked.

What is the Y-intercept? Why?

Practice Questions:

Cost depends on the number of minutes used.The domain values are the number of

minutes used and f(x) is the cost for those minutes.f(x) = $14 + .2x; solve for

$44What is the y intercept? Why?

Practice Questions:Graph the

following equation: y = -3x - 5

Write the equation for the graph

Find the missing coordinate of a line with

points (–2, R) and (4, 6) and a slope of32

Practice Questions:

If (a,2) is a point on the graph of 2x - 7y =

20, what is a?

R = -3

When to use the point-slope form of a line:a. If all you have to work with is one

point on the line and the slope of the line

b. If all you have are two points on the line

Write the equation of a line passing through

the point (2,5) with a slope of -2

20

Example: Write the equation of the line through the points (4, 3) and (-2, 5).

y – y1 = m(x – x1) Point-slope form

Slope-intercept formy = - x + 13

31

3

2 1 5 – 3 -2 – 4

= - 6

= - 3

Calculate the slope.m =

Use m = - and the point (4, 3).y – 3 = - (x – 4)1

3 3

1

Find the x-intercept of the line with slope of 2 and passing through the points (-1, 2)

and (0,4)

21

Write the standard form for the equation of the line through the point (-2, 5) with a slope of 3.

Use the point-slope form, y – y1 = m(x – x1), with m = 3 and (x1, y1) = (-2, 5). y – y1 = m(x – x1) Point-slope form

y – y1 = 3(x – x1) Let m = 3.

y – 5 = 3(x – (-2)) Let (x1, y1) = (-2, 5).

y – 5 = 3(x + 2) Simplify.

y = 3x + 11 Slope-intercept form

3x – y = - 11 Standard Form

Find the equation of the line that has a slope of and a y-intercept of 2. Graph the line and write the equation in both slope-intercept and standard forms with integers only. The Graph

The Equations

1. Slope-intercept form: The instant equation, just add x and y. Fractional form: y = x + 2

Integer form form: 4y = x + 8 2. Standard Form: Easily & directly found by

doing this: cross-multiply

The Other Formulas

Find the equation of the line that has a slope of and a y-intercept of -1. Graph the line and write the equation in both slope-intercept and standard forms with integers only for the standard form.

On Your Own:

What if:The only information you have is the slope , and a point on the line, (1,2). Use the correct equation & graph the line. Then write the equation in standard form with integers only.

You begin with the point-slope formula, which becomes the slope-intercept form. Use the slope-intercept to graph.To put the equation in standard form, you can do this...

Class Work 2.11; Due @ Beginning

of Class Tomorrow Show All Work