Summary: Graphing a Line

Graphing a Line                                                                 January 3, 2012

OBJECTIVE: SWBAT GRAPH LINES ON A COORDINATE PLANE TO CREAT A SYSTEM

Today in class we learned/reviewed about how to graph a line and what you need to graph a line. To graph a line, you need a slope, which is change in y over change in x, b, your y intercept, and two points. You actually don’t really need the first two, y; you just need the two points to find you slope, which you could then use to find your y intercept, and then you could graph your line. Other ways to find your y intercept would be to use point slope or to graph the line or to navigate using the slope.

Summary: Systems of Equations- Elimination

Systems of Equations- Elimination                                   December 1, 2011

OBJECTIVE: SWBAT SOLVE SYSTEMS BY GRAPHING, ELIMINATION AND SUBSTITUTION

Today in class we learned about elimination. Elimination is fairly easy; all you need to do is choose a variable that you would want to cancel out. Usually you would want to use the easiest variable that you can eliminate. To eliminate that variable you would have to multiply the variable that you would want to eliminate with the other equation. Once you eliminated that equation, you solve it. An example is shown below.

EXAMPLE:

Summary: Systems of Equations- Graphing

Systems of Equations- Graphing                                November 28, 2011

OBJECTIVE: SWBAT SOLVE SYSTEMS BY GRAPHING, ELIMINATION AND SUBSTITUTION 

Today we learned about the three different types of systems of equations. The three methods are graphing, elimination and substitution. When graphing, always convert equations to y=mx+b. When you graph both lines, look for the point of intersection. This point is your solution set. A solution set is a solution to the equations that you graphed; it must satisfy both. Parallel lines have no solution; they have a solution, but they don’t share the same solution. You graphing your lines you should start labeling them. An example is shown below.

EXAMPLE:

Summary: Systems of Equations- Substitution

Systems of Equations- Substitution                        November 28, 2011

OBJECTIVE: SWBAT SOLVE SYSTEMS BY GRAPHING, ELIMINATION AND SUBSTITUTION

Today we learned about the three different types of systems of equations. The three methods are graphing, elimination and substitution. Today we focused on substitution and graphing. For substitution, it might be easier to use different colors and draw lines to separate the parts you have already done. You don’t have to do this; this is optional, but this usually helps others. There are four steps to remember when doing substitution. 1) Pick a variable-either x or y; 2) Solve the variable; 3) Substitute into an equation; 4) Combine Like Terms- CLT. An example is shown below on how to do this.  

EXAMPLE:

Summary: Scatter Plots and Trend Lines

Scatter Plots and Trend Lines                                         November 1, 2011

OBJECTIVE: SWBAT DISCUSS TRENDS AND TREND LINES; IDENTIFY SCATTER PLOTS

Today we learned about scatter plots, trends and trend lines. Scatter plots and trend lines are like correlations. Correlations are how things are related to each other. Scatter plot is a graph of scattered points and trend line is drawing a line in the middle of all the scattered points. Basically, you want to include as most of the dots as possible. To know if the trend line is positive, the change in y and the change in x is either both positive or both negative. The trend line is negative if the change in y is positive and the change in x is negative. An example is shown below.

EXAMPLE:

Summary: Continuous and Discrete

Continuous and Discrete                                                                  October 27, 2011

OBJECTIVE: SWBAT DIFFERENCIATE BETWEEN CONTINUOUS/ DISCRETE

Today we learned about continuous and discrete. Discrete means that the item has to be a whole number. Discrete usually occurs when we are counting using whole numbers. Continuous can be fractional numbers and whole numbers. Basically, something that is measurable: height, weight, and time. If the numbers can be fractions and decimals then it is probably continuous. Some examples are shown below.

EXAMPLE:

Classify each set as discrete or continuous-

1. The number of suitcases lost by an airline.

2. The height of corn plants.

3. The number of ears of corn produced.

4. The number of green M&M’s in a bag.

5. The time it takes for a car battery to die.

6. The Production of tomatoes by weight.

1) Discrete. The number of suitcases lost must be a whole number.

2) Continuous. The height of corn plants can take on infinitely many values (any decimal is possible).

3) Discrete. The number of ears of corn must be a whole number. 

4) Discrete. The number of green M&M's must be a whole number. 

5) Continuous. The amount of time can take on infinitely many values (any decimal is possible).

6) Continuous. The weight of the tomatoes can take on infinitely many values (any decimal is possible). 

Summary: Shading Inequalities

Shading Inequalities                                                                 October 25, 2011

OBJECTIVE: SWBAT RECALL INEQUALITIES AND HOW TO SOLVE THEM

Today we learned more about inequalities and about how to shade the graph. For shading a graph, you either shade with or without the point you are using to substitute it in an equation. For example, let’s use the inequality y<4x-3. For x and y we will substitute in the points (0, 0). Now the equation reads 0<4(0)-3. Solve that and it reads 0<-3. If this inequality is true then you will shade the part that INCLUDES the points (0, 0). If the inequality is false then you would shade AWAY from the point.

EXAMPLE:

y<4x-3

Summary: Graphing Inequalities

Graphing Inequalities                                                                 October 25, 2011

OBJECTIVE: SWBAT RECALL INEQUALITIES AND HOW TO SOLVE THEM

Today we learned more about inequalities and about how to graph them. We learned that for inequalities with < and > that they had a dashed line. Then for ≤ and ≥ they have solid, as well as =. Graphing inequalities is actually easy. You graph it like a regular slope intercept equation. You just have to make the “y” an isolated variable as it is in slope intercept form. An example is shown below.

EXAMPLE:

y+3<4x à y<4x-3

Summary: Inequalities

Inequalities                                                                 October 24, 2011

OBJECTIVE: SWBAT RECALL INEQUALITIES AND HOW TO SOLVE THEM

Today we relearned inequalities. I actually remembered this from when we were in sixth grade and that all we had to do was just remember what the sign were. Those signs were: less than of equal to (≤), less than (<), greater than or equal to (≥), and greater than (>). We also learned that when you graph inequalities, you use a dashed line, not a regular line. Also we learned that when you’re writing inequalities on the number line there are open and closed circles. Open circles mean less than or greater than and closed circles mean it has the equal to part with it. An example is shown below.

EXAMPLE:

  3 ≤ x-2 ----------------------------> Your Problem

+2   +2-----------------------------> Add 2 to 3 and -2

5 ≤ x -----------------------> Answer used to graph on number line

Summary: Linear Equations

Linear Equations                                                                 October 13, 2011

OBJECTIVE: SWBAT WRITE, GRAPH, AND CREATE LINEAR EQUATIONS IN THE THREE FORMS

Basically all we did was review slope intercept (SI), point slope (PS), and standard form (STD). Along with that, we practiced changing from one form to another. For example, we did a problem for PS then changed it to SI then changed it to STD. Now, changing from PS to SI is quite easy actually but, changing from SI to STD. Now, that is a whole another story because I get it but, then I don’t get it. It looks hardier than it actually is but, I think I can manage to it.

EXAMPLE:

(3, 4) b=-5

1. Point Slope (PS)-

*To find your slope do y1-y2 over x1-x2, when you have two points*

-5-4/0-3 equals -9/-3 which equals positive 3

Now just substitute the numbers into the formula-

y-4=3(x-3)

2. Slope Intercept (SI)-

*Substitute in the numbers for slope and y-intercept*

y=3x-5

3. Standard Form (STD)-

*If your slope is positive the y will be negative*

**If your y is negative then C might be positive**

3x 1y=

Now, just figure out the sign and if the C is negative or positive

3x-1y=5 or 3x-y=5

   -y is negative because it will then make -3x positive and make 5 negative