Algebra 1 Common Core Answers Student Edition Grade 8 – 9 Chapter 1 Foundations for Algebra Exercise 1.9
Algebra 1 Common Core Answers Student Edition Grade 8 – 9
Chapter 1 Foundations for Algebra Exercise 1.9 1LC
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The objective is to differentiate between inductive and deductive reasoning.
Inductive reasoning is the process of reaching a conclusion that starts with an observed pattern. It is based on the assumption that the observed pattern continues. So, the conclusion may not be always true in real world.
On the other side, deductive reasoning is the process of reaching a conclusion logically that starts with rules that are true. So, the conclusion must be true.
Chapter 1 Foundations for Algebra Exercise 1.9 6LC
The objective is to find the similarity and difference between writing an equation to represent a situation involving two variables and writing an equation to represent a situation involving only one variable.
One similarity is that each equation contains unknown value(s).
One difference is that one of them contains only a single variable and the other is a relation connecting two variables.
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Consider the pattern “Each packet contains 12 pencils”.
So, the number of pencils is affected by the number of packets. To find the total number of pencils in a number of packets, you need to multiply the number of packets and the number of pencils contained in each packet. For example, the total number of pencils in 5 packets is.
Two variables are required to represent the pattern using an equation, one that represent number of packets and another that represent number of pencils.
Let x represent number of packets and y represent number of pencils.
Since each packet contains 12 pencils, y is always 12 times x.
So, the equation that represents the pattern is, where x denoting number of packets y denoting number of pencils.
Chapter 1 Foundations for Algebra Exercise 1.9 34E
Consider the pattern “Temperature risesevery 45 min”.
Suppose that the starting temperature is.
The aim is to represent the pattern using a table, an equation, and a graph.
Note that,
So, if the number of hours increases by, the temperature will be increase by.
To represent the pattern using a table, draw two rows having a number of columns.
Label the first row “Hours (h)” and the second row “Temperatures”.
Put the valuesin the first row.
Two variables are required to represent the pattern using an equation, one that represents hours and another that represents temperatures in.
Let x represent hours and y represent temperature in.
Replace the labels in the table by the variables.
Looking at the above table, you can see that y is always 60 more thantimes x.
So, the equation that represents the relationship is, where x denoting number of hours and y denoting temperatures in.
After converting the fractions into decimals, the ordered pairsrepresented by the table are:
To represent the relationship using a graph, plot the ordered pairs on a coordinate plane and connect them by a straight line.
Extend the line on both sides and add arrow(s) to show that the line continues infinitely.
Chapter 1 Foundations for Algebra Exercise 1.9 35E
Consider the ordered pairs:
The aim is to represent the ordered pairs using a table, a graph, and an equation.
In an ordered pair, the first value is the x-coordinate and the second value is the y-coordinate.
For example, the x- and y-coordinates of the first ordered pairare 2 and -5.5 respectively.
To represent the ordered pairs using a table, draw two rows having a number of columns.
Label the first row “x” and the second row “y”.
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