for the linear functions that give the following tables and graphs For the graphs assume a scale of 1 for each axis Find the line of best fit for east and westbound flights Predict the amount of time for a flight from Chicago to Durham which is a distance of 647 ID: 557817
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Slide1
Write rules in the form for the linear functions that give the following tables and graphs. For the graphs, assume a scale of 1 for each axis.
Slide2
Find the line of best fit for east and westbound flightsPredict the amount of time for a flight from Chicago to Durham, which is a distance of 647 mi.Slide3
The reasoning for solving linear equations also applies to solving linear inequalitiesDirection of the inequality does matterWhile is the same as
, is not the same as
Question of the day: How can we solve a linear inequality algebraically?
Slide4
Property of an InequalityWhat happens when we multiply both sides of an inequality by a negative number?Multiply both sides of the following inequalities by
, then indicate the relationship between the numbers using < or >
Based on observations from A, complete the statements:
If
, then
.
If
, then
.
Slide5
For each pair of numbers below, describe how it can be obtained from the pair above it. Then, indicate whether the direction of the inequality stays the same or reverses.
9 > 4
12
>
7
24
>
14
20
?
10
-4
? -2-2 ? -18 ? 46 ? 2-18 ? -63 ? 121 ? 7
Operation Add 3 .Multiply by 2________________________________________________________________________________________________
Direction
Stays the same
Stays the same
_____________
_____________
_____________
_____________
_____________
_____________
_____________
_____________Slide6
For each pair of numbers below, describe how it can be obtained from the pair above it. Then, indicate whether the direction of the inequality stays the same or reverses.
9 > 4
12
>
7
24
>
14
20
>
10
-4
< -2-2 < -18 > 46 > 2-18 < -63 > 121 > 7
Operation Add 3 .Multiply by 2 Subtract 4 . Divide by -5. Divide by 2 .Multiply by -4 Subtract 2 .Multiply by -3 Divide by -6. Multiply by 7
Direction
Stays the same
Stays the same
Stays the same
Reverses .
Stays the same
Reverses
.
Stays the same
Reverses
.
Reverses
.
Stays the sameSlide7
Look back at your answers to the previous problem, and identify cases where operations reversed the direction of the inequality.What operations seem to cause the reversal of inequality relationships?Why does it make sense for these operations to reverse inequality relationships?Slide8
Look back at your answers to the previous problem, and identify cases where operations reversed the direction of the inequality.What operations seem to cause the reversal of inequality relationships? Multiplication or division by a negative number
Why does it make sense for these operations to reverse inequality relationships? Can subtract each side to the opposite side, which has the same effect as multiplying or dividing by -1
Slide9
Recall from PreviouslyThe trends shown can be modeled with the following functions:Percent male doctors:
Percent female doctors:
represents time after 1960
Ex. For the year 1970,
Slide10
A class was asked, “For how long will the majority of U.S. doctors be male?Taylor wrote this inequality:
Jamie wrote this inequality:
Explain the reasoning Jamie may have used for her inequality. Do you think the solution to either inequality will answer the question? Why or why not?
Solve the inequality you think is appropriate. Tell what you think this solution indicates.
Slide11
Taylor wrote this inequality: Jamie wrote this inequality:
Taylor and Jamie’s solutions are given below. Which answer makes more sense? Why?
What is the error in the incorrect solution?
Slide12
Solve the following linear inequalities. Pay careful attention to the direction of the inequality. Be sure to check you solutions.
Slide13
Think About ItLinear inequalities are usually pretty easy to solve once they’re set up.Suppose you are going to tell someone how to solve an equation like
algebraically. What steps would you recommend? Why?How would you check the solution to an inequality like
? Like
?
How is solving a linear inequality similar to, and different from, solving a linear equation?
When would you recommend solving an inequality algebraically? How about with a table? With a graph?