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Find the equations of the lines and plot the lines from Exercise $54$.

$y=24 x-9$

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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Find the equations of the …

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Find the equation of the l…

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Equations of Lines Find an…

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Finding an Equation of a L…

this exercise is going to reference information from exercise number 54 from earlier in this problem set if you go back and look at 54 we were given two points, zero negative nine and one half three. And in that problem, we found the slope of the line connecting those points to be 24. So that's our background information for this problem. We want to find the equation that this information represents, and then we're gonna graph that line on our grid. Now, there are two different ways we can go about fighting this equation. One way is the slope intercept form Y equals MX plus B because we were fortunate enough to be actually given the y intercept. Okay, so if I wanted to use this equation, I could pull my slope, which is 24 and the y coordinate of that y intercept, which is negative. Nine. That's a pretty easy way to find the equation. But we just got lucky. We often don't have that y intercept. So how could we do this if we didn't have the y intercept? Well, we could use another form, which is the point slope form, So that's why minus why one equals M times X minus X one. So let's use our other point. And we're just going to show that no matter which way you do this, you'll end up with the same answer. So why minus the Y? Coordinate, that's three. My slope is 24 x minus The X coordinate. That's a half. So have Y minus three. I wanna get rid of my parentheses. That's 24 X minus 12. And then if I add three to both sides, I end up with the exact same line, Which makes sense. It's the same points. It's the same slope. It should be the same equation. Now, this is gonna be kind of tricky to graph on here because that slope of 24 is very, very, very steep. Eso we're going to just do the best we can graphic this. First of all, I could put on my Y intercept Negative nine. So 12345678 green dot Right there, There's my Y intercept now, my slope 24th positive. So it's going to be going up as I go from left to right. My life should be trending upward and my slope, my rise over run rise over run is 24/1, so I'm going to rise 24 units to just go over one. So let's see if I could actually rise 24 say on my grid here. That's nine to the origin. 10 11 12 13 14 15 16 17 18 1920 22 23. I am actually just above the next line up would be 24. So there's my two lives. This one is going to be very difficult to actually draw and make it nice and straight. If you have a ruler, that's definitely gonna help with this because those points are so far apart. But that's the graph of this equation. Why equals 24 x minus nine.

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