8 Plot Points

Solutions to Equations with Two Variables

• The Magnificent 7 Plot Points There are five additional plot points you’ll need to apply, making seven in all. Since there will be many plot points in a movie, I call these The Magnificent 7 Plot Points. They are: the Back Story, the Catalyst, the Big Event (we’ve mentioned that one), the Midpoint, the Crisis, the Climax, and the Realization.
• Graph Individual (x,y) Points - powered by WebMath. The most basic plotting skill it to be able to plot x,y points. This page will help you to do that.

The Seven Basic Plots: Why We Tell Stories is a 2004 book by Christopher Booker containing a Jung-influenced analysis of stories and their psychological meaning.Booker worked on the book for thirty-four years. The screenplay expert who posted these well-constructed 8 plot points NEVEr said anything about applying these plot points to every single film there is and has ever been made out there in world! The 8 plot points are a general structure of plots that is commonly applied to MOST films, not an exact blueprint to every single film ever, you idiot!

A linear equation with two variables has standard form (ax+by=c), where (a,b), and (c) are real numbers and (a) and (b) are not both (0). Solutions to equations of this form are ordered pairs ((x, y)), where the coordinates, when substituted into the equation, produce a true statement.

Example (PageIndex{1})

Determine whether ((1, −2)) and ((−4, 1)) are solutions to (6x−3y=12).

Solution:

Substitute the (x)- and (y)-values into the equation to determine whether the ordered pair produces a true statement.

(begin{array}{c c}{underline{Check::(1,-2)}}&{underline{Check::(-4,1)}}{6x-3y=12}&{6x-3y=12} {6(color{OliveGreen}{1}color{black}{)-3(}color{OliveGreen}{-2}color{black}{)=12}}&{6(color{OliveGreen}{-4}color{black}{)-3(}color{OliveGreen}{1}color{black}{)=12}}{6+6=12}&{-24-3=12}{12=12quadcolor{Cerulean}{checkmark}}&{-27=12quadcolor{red}{x}}end{array})

Answer:

((1,-2)) is a solution, and ((-4,1)) is not.

It is often the case that a linear equation is given in a form where one of the variables, usually (y), is isolated. If this is the case, then we can check that an ordered pair is a solution by substituting in a value for one of the coordinates and simplifying to see if we obtain the other.

Example (PageIndex{2})

Are ((frac{1}{2}, −3)) and ((−5, 14)) solutions to (y=2x−4)?

Solution:

Substitute the (x)-values and simplify to see if the corresponding (y)-values are obtained.

(begin{array}{c c} {underline{x=frac{1}{2}}}&{underline{x=-5}}{y=2x-4}&{y=2x-4}{=2color{black}{left(color{OliveGreen}{frac{1}{2}} right)-4}}&{=2(color{OliveGreen}{-5}color{black}{)-4}}{=1-4}&{=-10-4}{=-3quadcolor{Cerulean}{checkmark}}&{=-14quadcolor{red}{x}} end{array})

Answer:

((frac{1}{2},-3)) is a solution, and ((-5,14)) is not.

Exercise (PageIndex{1})

Is ((6, −1)) a solution to (y=−frac{2}{3}x+3)?

Yes

When given linear equations with two variables, we can solve for one of the variables, usually (y), and obtain an equivalent equation as follows:

(begin{aligned} 6x-3y&=12 6x-3ycolor{Cerulean}{-6x}&=12color{Cerulean}{-6x}&color{Cerulean}{Subtract:6x:from:both:sides.} -3y&=-6x+12 frac{-3y}{color{Cerulean}{-3}}&=frac{-6x+12}{color{Cerulean}{-3}} &color{Cerulean}{Divide:both:sides:by:-3.} y&=frac{-6x}{-3}+frac{12}{-3}&color{Cerulean}{Distribute:and:divide.} y&=2x-4 end{aligned})

Written in this form, we can see that (y) depends on (x). Here (x) is the independent variable and (y) is the dependent variable.

(left. begin{aligned} 6x-3y&=12 y&=2x-4end{aligned}right} color{Cerulean}{Equivalent:equations})

The linear equation (y=2x−4) can be used to find ordered pair solutions. If we substitute any real number for (x), then we can simplify to find the corresponding y-value. For example, if (x=3), then (y=2(3)−4=6−4=2), and we can form an ordered pair solution, ((3, 2)). Since there are infinitely many real numbers to choose for (x), the linear equation has infinitely many ordered pair solutions ((x, y)).

Example (PageIndex{3})

Find ordered pair solutions to the equation (5x−y=14) with the given (x)-values ({−2, −1, 0, 4, 6}).

Solution:

First, solve for (y).

(begin{aligned} 5x-y&=14 5x-ycolor{Cerulean}{-5x}&=14color{Cerulean}{-5x} -y&=-5x+14 color{Cerulean}{-1}color{black}{(-y)}&=color{Cerulean}{-1}color{black}{(-5x+14)} y&=5x-14 end{aligned})

Next, substitute the (x)-values in the equation (y=5x−14) to find the corresponding (y)-values.

Answer:

({(−2, −24), (−1, −19), (0, −14), (4, 6), (6, 16)})

In the previous example, certain (x)-values are given, but that is not always going to be the case. When treating (x) as the independent variable, we can choose any values for (x) and then substitute them into the equation to find the corresponding (y)-values. This method produces as many ordered pair solutions as we wish.

Example (PageIndex{4})

Find five ordered pair solutions to (6x+2y=10).

Solution:

First, solve for (y).

(begin{aligned} 6x+2y&=10 6x+2ycolor{Cerulean}{-6x}&=10color{Cerulean}{-6x} 2y&=-6x+10 frac{2y}{color{Cerulean}{2}}&=frac{-6x+10}{color{Cerulean}{2}} y&=frac{-6x}{2}+frac{10}{2} y&=-3x+5 end{aligned})

Next, choose any set of (x)-values. Usually we choose some negative values and some positive values. In this case, we will find the corresponding (y)-values when (x) is ({−2, −1, 0, 1, 2}). Make the substitutions required to fill in the following table (often referred to as a t-chart):

Answer:

({(−2, 11), (−1, 8), (0, 5), (1, 2), (2, −1)}). Since there are infinitely many ordered pair solutions, answers may vary depending on the choice of values for the independent variable.

Exercise (PageIndex{2})

Find five ordered pair solutions to (10x−2y=2).

({(−2, −11), (−1, −6), (0, −1), (1, 4), (2, 9)}) (answers may vary)

We can use Excel to plot XY graph, also known as scatter chart or XY chart. With such charts, we can directly view trends and correlations between the two variables in our diagram. In this tutorial, we will learn how to plot the X vs. Y plots, add axis labels, data labels, and many other useful tips.

Figure 1 – How to plot data points in excel

Excel Plot X vs Y

We will set up a data table in Column A and B and then using the Scatter chart; we will display, modify, and format our X and Y plots.

• We will set up our data table as displayed below.

Figure 2 – Plotting in excel

• Next, we will highlight our data and go to the Insert Tab.

Teaching Plot Powerpoint

Figure 3 – X vs. Y graph in Excel

• If we are using Excel 2010 or earlier, we may look for the Scatter group under the Insert Tab

• In Excel 2013 and later, we will go to the Insert Tab; we will go to the Charts group and select the X and Y Scatter chart. In the drop-down menu, we will choose the second option.

Figure 4 – How to plot points in excel

• Our Chart will look like this:

Figure 5 – How to plot x and y in Excel

Add Axis Titles to X vs Y graph in Excel

• If we wish to add other details to our graph such as titles to the horizontal axis, we can click on the Plot to activate the Chart Tools Tab. Here, we will go to Chart Elements and select Axis Title from the drop-down lists, which leads to yet another drop-down menu, where we can select the axis we want.

Figure 6 – Plot chart in Excel

• If we add Axis titles to the horizontal and vertical axis, we may have this

Figure 7 – Plotting in Excel

Add Data Labels to X and Y Plot

We can also add Data Labels to our plot. These data labels can give us a clear idea of each data point without having to reference our data table.

• We can click on the Plot to activate the Chart Tools Tab. We will go to Chart Elements and select Data Labels from the drop-down lists, which leads to yet another drop-down menu where we will choose More Data Table options

Figure 8 – How to plot points in excel

• In the Format Data Table dialog box, we will make sure that the X-Values and Y-Values are marked.

Figure 9 – How to plot x vs. graph in excel

• Our chart will look like this;

Figure 10 – Plot x vs. y in excel

• To Format Chart Axis, we can right click on the Plot and select Format Axis

Figure 11 – Format Axis in excel x vs. y graph

• In the Format Axis dialog box, we can modify the minimum and maximum values.

Figure 12 – How to plot x vs. y in excel

Plot Points Film

• Our chart becomes;

Figure 13 – How to plot data points in excel

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8 Plot Points Screenwriting

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