<caption><image_0>The image is a title slide for a presentation on the graph of a line. The title is written in blue text on a white background. Below the title, there is a subtitle that reads "The Graph of a Line" in black text. On the right side of the slide, there are two lines, one in red and one in blue, intersecting at the top and bottom of the image. The red line is a triangle with a point at the center and a line at the bottom, while the blue line is an angle at the end. The line is curved and appears to be made up of two intersecting points. The image also has a small logo in the bottom right corner.</caption><transcript><audio_1>tres is saying that a picture is worth a thousand words now since this video is running by at 24 pictures per second that means you've just seen a novel although since it's been the same picture the novel's are</transcript><transcript><audio_2>pretty boring one but I digress let's talk about the mathematical equivalent of a picture the graph of a line now remember that any point in the plane can be specified by its coordinates x and y</transcript><transcript><audio_3>for example I might try to sketch the graph of the following set of coordinates 1 3 1 5 + 2 4 so this first set of coordinates 1 3 specifies a point</transcript><caption><image_4>The image is a screenshot of a text-based question. The text is written in a simple, sans-serif font and is centered on the screen. Below the text, there is a green rectangle with the word "Example" written in it. The rectangle is labeled "Sketch the graph of" and has a value of "G = (1,0,0.5,5,2,0)". The background of the image is white.</caption><transcript><audio_5>that has x-coordinate 1 and y coordinate so we'll plot that point but we'll also label its coordinates a good habit to get into next I'll sketch dissapoint</transcript><transcript><audio_6>with x coordinate 1 y coordinate 5 and finally the point with x-coordinate - y-coordinate for now it's important to understand that because our graph is given as these three points only then</transcript><transcript><audio_7>our graph consists of these three points only sometimes we have too many points to list them conveniently and so instead we represent the graph by rating the</transcript><caption><image_8>The image is a screenshot of a webpage with a white background. The title of the webpage is "Graphs and Equations" and it appears to be a question or answer. Below the title, there is a text that reads "Sometimes we have two many points to let commonly". The text is written in black font and is centered on the page.</caption><transcript><audio_9>relation between the x and y values for example I might say something like this suppose the Y values of a point on the graph are three times the X values first of all we want to express this as an equation and then find three points on</transcript> tres is saying that a picture is worth a thousand words now since this video is running by at 24 pictures per second that means you've just seen a novel although since it's been the same picture the novel's are pretty boring one but I digress let's talk about the mathematical equivalent of a picture the graph of a line now remember that any point in the plane can be specified by its coordinates x and y for example I might try to sketch the graph of the following set of coordinates 1 3 1 5 + 2 4 so this first set of coordinates 1 3 specifies a point that has x-coordinate 1 and y coordinate so we'll plot that point but we'll also label its coordinates a good habit to get into next I'll sketch dissapoint with x coordinate 1 y coordinate 5 and finally the point with x-coordinate - y-coordinate for now it's important to understand that because our graph is given as these three points only then our graph consists of these three points only sometimes we have too many points to list them conveniently and so instead we represent the graph by rating the relation between the x and y values for example I might say something like this suppose the Y values of a point on the graph are three times the X values first of all we want to express this as an equation and then find three points on
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