To graph a negative slope, apply the same rise/run principle that you'd apply for a positive slope. Instead of going up and to the right, you will go down or to the left, depending on whether the numerator or denominator is negative. For example, if you were graphing y = -5/3x, you would start by going to (0,-5) and plot your first point at (3,-5). Go down another 5 and over another 3 from there, and so on. Show Expert AnswersWhen graphing a linear equation, slope refers to the value m in the equation y = mx + b. For example, if you had to graph the linear equation y = 5x, your slope would be 5. When graphing a slope, it is useful to apply the idea of rise... Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel
anytime. Already a member? Log in here. When graphing a linear equation, slope refers to the value m in the equation y = mx + b. For example, if you had to graph the linear equation y = 5x, your slope would be 5. When graphing a slope, it is useful to apply the idea of rise over run. This means that you view slope as a fraction, and go up or down (rise) the number of points in the numerator and then go left or right (run) the number of points in the denominator. For example, in the above equation, 5 is the same as saying 5/1, so you would start at (0,0), go up 5 points on the y-axis, and over to the right 1 point on the x-axis. Here, at (1,5) is where you would plot your first point. Then from that point, you would do the same thing again. Up another 5, over to the right another 1. Once you have enough points, you will begin to see a line. You should take the same approach when graphing a negative slope. For example, let’s say you have to graph the following linear equation: y = -5/3x In this case, instead of starting from (0,0) and going up 5 points, you would start from (0,0) and go down 5 points because the slope is not positive. Now the 3 in the denominator is positive, which means you still go to the right 3 points. So your first point should be at (3, -5). Note that you would still end up with the same line if you put the negative sign in the denominator and not the numerator. For example, you could start at (0,0) and go up 5 points, and then go left 3 points if the 3 was negative. This would make your first point (-3, 5). Eventually, after plotting enough points with this rise/run method, you would get the same line. Approved by eNotes Editorial Team Math Latest answer posted September 07, 2010 at 12:47:25 PM 14 Educator answers Math Latest answer posted November 14, 2011 at 5:49:28 AM 1 Educator answer Math Latest answer posted August 17, 2010 at 8:49:11 AM 8 Educator answers Math Latest answer posted November 27, 2012 at 2:59:10 PM 1 Educator answer Math Latest answer posted October 09, 2017 at 12:54:39 AM 3 Educator answers Video transcriptFind the slope of the line pictured on the graph. So the slope of a line is defined to be rise over run. Or you could also view it as change in y over change in x. And let me show you what that means. So let's start at some arbitrary point on this line, and they highlight some of these points. So let's start at one of these points right over here. So if we wanted to start one of these points-- and let's say we want to change our x in the positive direction. So we want to go to the right. So let's say we want to go from this point to this point over here. How much do we have to move in x? So if we want to move in x, we have to go from this point to this point. We're going from negative 3 to 0. So our change in x-- and this triangle, that's delta. That means "change in." Our change in x is equal to 3. So what was our change in y when our change in x is equal to 3? Well, when we moved from this point to this point, our x-value changed by 3, but what happened to our y-value? Well, our y-value went down. It went from positive 3 to positive 2. Our y-value went down by 1. So our change in y is equal to negative 1. So we rose negative 1. We actually went down. So our rise is negative 1 when our run-- when our change in x-- is 3. So change in y over change in x is negative 1 over 3, or we could say that our slope is negative 1/3. Let me scroll over a little bit. It is negative 1/3. And I want to show you that we can do this with any two points on the line. We could even go further than 3 in the x-direction. So let's go the other way. Let's start at this point right over here and then move backwards to this point over here, just to show you that we'll still get the same result. So to go from this point to that point, what is our change in x? So our change in x is this right over here. Our change in x is that distance right over there. We started at 3, and we went to negative 3. We went back 6. Over here, our change in x is equal to negative 6. We're starting at this point now. So over here our change in x is negative 6. And then when our change in x is negative 6, when we start at this point and we move 6 back, what is our change of y to get to that point? Well, our y-value went from 1. That was our y-value at this point. And then when we go back to this point, our y-value is 3. So what did we do? We moved up by 2. Our change in y is equal to 2. Slope is change in y over change in x, or rise over run. Change in y is just rise. Change in x is just run, how much you're moving in the horizontal direction. So rise over run in this example right over here is going to be 2 over negative 6, which is the same thing as negative 1/3. And you could verify it for yourself. Take any of these two points, start at one of these two points, and figure out what is the run to get to the next point, and then what is the rise to get the next point. And for any line, the slope won't change. Let me do it again. Over here, we had to move in the positive 3 direction, so that is our run. So this right here is positive 3. That's our run. But what's our rise? Well, we actually went down, so we have a negative rise. Our rise is negative 1. So we have negative 1 as our rise. We went down. And our run was positive 3. So our slope here is negative 1/3. How do you graph a negative slope?Example 2: Graphing a Negative Slope. Plot the 1st point. ( 0,7). Count the rise. (We went down 3 since the slope was negative.. Count the run. ( The denominator is 1, so we went right 1). Plot the 2nd point.. Repeat the process if you'd like to plot a 3rd point.. Draw a line through your points.. Can a slope be a negative fraction?To get from point A to point B, you need to take one step down and two steps to the right. The slope equals. When calculating a slope, the negative may appear in the numerator or the denominator. A negative slope is typically written with the negative in front of the fraction.
|
How to graph a negative fraction slope
Related Posts
Copyright © 2024 paraquee Inc.
