Graphing Linear Equations 04:31 minutes

Video Transcript

Transcript Graphing Linear Equations

Dr. Evil is in his elegant lair busily hatching another especially evil plot. This time, he’s after some information stored on General Good’s computer. To steal the data, he plans to use C.H.E.E.S.E.1, a computer hacking drone.

Before Dr. Evil can launch his plan, there are some problems he must solve. C.H.E.E.S.E.1 can copy data at a speed of one point two-five petabytes per second.

Dr. Evil has been surveilling General Good and knows that every day, exactly at midnight, General Good opens the window and goes into the hallway to stretch for 60 seconds. So the drone will have just sixty seconds to download all of the data. The problem is, can C.H.E.E.S.E.1 complete the task in time?

Writing the Linear Equation in Slope-Intercept Form

You may ask, how can Dr. Evil solve this problem? He can graph linear equations using slope-intercept form. Let’s take a look at the coordinate system.

The file he plans to steal is ninety petabytes. The drone has exactly sixty seconds to copy all of the data and the hacking program loaded on C.H.E.E.S.E.1 takes up 15 petabytes of space. The drone will have a total of 105 petabytes of data after copying the wanted files, if the caper is successful.

Now, he writes the equation in slope-intercept form: y = mx + b. Remember, m = slope and b = y-intercept. For this equation, x represents the number of seconds it takes for the drone to download the data and y represents the total amount of data stored on the drone.

The drone can download 1.25 petabytes of data per second, so the coefficient – or the slope – of x is 1.25.

The hacking program loaded on C.H.E.E.S.E.1 takes up 15 petabytes of space. Since this number does not change, it's called a constant. It is also the y-intercept.

Putting all of this together, the equation in slope-intercept form is y = 1.25x + 15.

Graphing the Linear Equation

Dr. Evil graphs the equation. The line touches the y-axis at the y-intercept, 15. The slope is 1.25. To graph this, write this decimal as a fraction. So the slope is 5/4, which means that the line rises 5 and runs 4. Dr.

Evil needs to know if C.H.E.E.S.E.1 do the task. Oh no! The line doesn’t go through the ordered pair of (60, 105) representing sixty seconds and 105 petabytes, respectively.

C.H.E.E.S.E.1 is too slow. What can Dr. Evil do? Dr. Evil has a plan B. He can use MAC2, a faster version. It’s a bit of a risk cause MAC2 is a beta version, but Dr. Evil is desperate. MAC2 has a download speed of one point 75 petabytes per second.

Using the download speed for MAC2, Dr. Evil writes a new equation in slope-intercept form. This time, the x coefficient, or slope, is equal to 1.75. The y-intercept does not change.

Dr. Evil gathers his evil data and draws an evil graph. The line still touches the y-axis at 15, but since the slope is 1.75 or 7 over 4 in fraction form, the line rises 7 and runs 4.

The graph indicates MAC2 can download 120 petabytes of data in sixty seconds. Dr. Evil is ecstatic! The graph shows MAC2 can do the task with seconds to spare!

Dr. Evil can’t wait to take a look at the data stolen from General Good. Oh no! What’s this? MAC2 copied the wrong file. Now, Dr. Evil’s computer is infected with the Kitty Cat virus. Meow!

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