Transcript TwMM 2.4 Solving Linear Functions rev.pptx

Math CC7/8 – Be Prepared
On Desk:
Learning Log:
1. Pencil
2. Calculator
3. Math Journal
4. TwMM Learning Log
1. HW: p. 49, #20, 21, #22-25
(a only!), #43
Tasks for Today
• Warm Up – Writing equations
• Lesson 2.4 – Inequalities, Solving Linear
Equations
Warm Up
Find an equation for the line that satisfies the conditions.
What are inequalities?
Symbol
Words
Example Use
=
≠
equals
not equal to
1+1=2
1+1≠1
>
<
greater than
less than
5>2
7<9
≥
greater than or equal to
marbles ≥ 1
≤
less than or equal to
dogs ≤ 3
What is an inequality?
• An inequality is similar to an equation.
• There are two expressions separated by a symbol that
indicates how one expression is related to the other.
• In an equation such as 7x = 49, the = sign indicates
that the expressions are equivalent.
• In an inequality, such as 7x > 49, the > sign indicates
that the left side is larger than the right side.
• To solve the inequality 7x > 49, we follow the same
rules that we did for equations.
• In this case, divide both sides by 7 so that x > 7. This
means that x is a value and it is always larger than 7,
and never equal to or less than 7.
$ 0.15 = the cost per minute of rental time
$2.50 = the fixed charge for renting
2. Use substitution!
c = 0.15t + 2.50
c = 0.15(25) + 2.50
c = $6.25
3. Solve for t…
$9.25 = 0.15t + 2.50
-2.50
- 2.50
6.75 = 0.15t
0.15 0.15
45 = t
$6
≥ 0.15t + 2.50
-2.50
- 2.50
3.50 ≥ 0.15t
0.15 0.15
23.3 ≥ t
Hint: Use an inequality!
She can use the canoe for no
more than 23 and 1/3 minutes,
or about 23 minutes or less.
• You can easily estimate the y-intercept. (2.50)
• You can use it to calculate the slope. (0.15)
• You can find 25 min on the x-axis and
estimate the cost from the y-axis.
• You can find $9.25 on the y-axis and estimate
the time for that charge.
• You can use it to find all the times that would
lead to a cost of no more than $6.
• You can calculate the slope by finding the change in y (rental charge) as x (time)
increases by 1 minute. (slope = 0.15)
• You could work backwards and find the y value for when x is 0. (y-intercept =
2.50)
• You can find the y-value (cost) for 25 min. by finding the point between 20 and
30 on the table.
• You can find the time for $9.25 by finding the point between 40 and 50 minutes.
• You can find the rental time for no more than $6 by looking at the rental charge
row and seeing it would be just over 20 minutes.
Yes, they are correct!
They subtracted 2.50 from each side of the equation
and then divided by 0.15 on each side of the equation.
She can use the canoe for no more than
23 and 1/3 min., or about 23 min. or
less.
Use substitution!
c = 4 + 0.10t
c = 4 + 0.10 (20)
c = $6
3. Solve for t…
$9 = 4 + 0.10t
-4 - 4
5 = 0.10t
0.10 0.10
50 = t
$12
≥ 4 + 0.10t
-4
-4
8
≥ 0.10t
0.10 0.10
80 ≥ t
You can use the paddle boat for
no more than 80 minutes, or an
hour and 20 minutes or less.
Hint: Use an inequality!