12-17 ParallelInequalitites

Question 1

What do Parallel Lines have in common?

Answer 1

They have the same slope.

Question 2

Given y = -3x + 5

find a Parallel Line that goes through (6,4)

Answer 2

(y - 4) = -3(x - 6)

y = -3x + 22

Question 3

How are Perpendicular Lines related?

Answer 3

The product of their slopes is -1.

Question 4

What is the slope of the line perpendicular to:

y = 2x + 1

Answer 4

2 * ? = -1

-½

Question 5

How do you find where these 2 lines intersect?

y = ⅔x + 1

y = ^-3/₂x - 4

Answer 5

Make them equal to each other and solve for x:

⅔x + 1 = ^-3/₂x - 4

¹³/₆x = -5

x = -5* ⁶/₁₃ = ^-30/₁₃ = -2 ⁴/₁₃

In either equation, when x = -2 ⁴/₁₃,

y = ^-7/₁₃

They intersect at (-2⁴/₁₃,^-7/₁₃)

Question 6

How do you use inverse equations to convert:

Fahrenheit ←→ Celcius?

Answer 6

F = C*1.8 + 32

^{Exchange F and C and solve for C}

::C = (F - 32)/1.8 or

C = (F - 32)*⁵/₉

_{because 1/1.8 = 5/9}

Question 7

What does Boyle’s Law say about altitude and temperature?

Answer 7

The boiling point of water depends on the altitude.

Question 8

If the boiling point of water at sea level is 100°, and the boiling point is 91.6° at 8000 feet,

what is the boilng point at 5280 ft.?

Answer 8

The slope is ^-8.4°/_8000ft.

:: (^-8.4°/_8000ft.)*5280 + 100

= 94.456°

Question 9

What is the best way to represent a Linear Inequality?

Answer 9

On a graph

Question 10

How do you prepare them for graphing?

Answer 10

Put in the y = form.

Question 11

Once you make the graph, how do you know where the region of the inequality is?

Answer 11

Check test points on either side of the line(s).

Question 12

How do you solve Linear Inequalities on TI nSpire?

Answer 12

menu → Algebra → Solve →

enter equation ^{(find inequality signs at ctrl/= button)}

after equation enter , then x →

Enter

Question 13

How do you graph Linear Equalities on TI Spire?

Answer 13

Go to graphing screen →

press tab for the space to enter the equation →

delete the = sign →

enter the equation

Question 14

Put the following in graphing form:

4x + 8y ≥ 10

Answer 14

8y ≥ 10 - 4x

y ≥ ⁵/₄ - ½x

Question 15

What do negative numbers do to inequalities?

Answer 15

They switch the sign.

5 < 8

-5 > -8

Question 16

What are the 2 forms of inequality notation?

Answer 16

-5 ≤ x ≤ 5

[-5, 5]

Question 17

What is the difference between () and []?

Answer 17

( ) does not include the end points.

[] does include the end points.

Question 18

How do you solve inequalities with Absolute Values?

|ax + b| > c

Answer 18

(1) First, drop the absolute value bars.
(2) Restate:

ax + b > c

ax + b < -c

(3) The range is between c and -c