So my change in y divided by change in x is two divided by two is one. So for this line I have slope is equal to one. But what would a slope of two look like? Well, a slope of two should be steeper and we can draw that. Let me start at a different point, so if I start over here a slope of two would look like This line right over here, you see it. If my change in x is equal to one, my change in y is two.
So change in y over change in x is gonna be two over one, the slope here is two. And now, hopefully, you're appreciating why this definition of slope is a good one.
The higher the slope, the steeper it is, the faster it increases, the faster we increase in the vertical direction as we increase in the horizontal direction. Now what would a negative slope be? So let's just think about what a line with a negative slope would mean. A negative slope would mean, well we could take an example. If we have our change in y over change in x was equal to a negative one.
Summary Slope. Page 1 Page 2. Slope In addition to its familiar meaning, the word "slope" has precise mathematical meaning. Previous section Problems Next page Slope page 2. Take a Study Break. Press ESC to cancel. Skip to content Home Physics What does a straight line with a negative slope mean? Ben Davis October 30, What does a straight line with a negative slope mean? What does it mean when velocity has a negative slope? What does a negative slope on a distance time graph mean?
Can a distance graph be negative? Slope The slope of a line measures the steepness of the line. Most of you are probably familiar with associating slope with "rise over run". Rise means how many units you move up or down from point to point. On the graph that would be a change in the y values. Run means how far left or right you move from point to point. On the graph, that would mean a change of x values. Here are some visuals to help you with this definition: Positive slope: Note that when a line has a positive slope it goes up left to right.
Negative slope: Note that when a line has a negative slope it goes down left to right. If you need more of a review on slope, feel free to go to Tutorial Equations of Lines. This form can be handy if you need to find the slope of a line given the equation.
When it is in this form it makes it easier to identify the slope and the y -intercept of the line. In this form, the slope is m , which is the coefficient in front of x and the y -intercept is the constant b. Step 2: Plot the y -intercept on a 2-dimensional graph. Recall that the y -intercept is where it crosses the y -axis. So x 's value will be 0. If you need more review on intercepts, feel free to go to Tutorial Equations of Lines. Step 3: Use the slope to find a second point on the line. You will start with the y -intercept and rise up or down and then run left or right depending on the sign of the slope.
What do you think is the positive direction for rise, up or down? If you said up, pat yourself on the back. That means down is the negative direction for rise. A way to remember this is to think about the numbers are on the y -axis. Going up above the origin are the positive values, and going down below the origin are the negative values.
What do you think is the positive direction for run, right or left? If you said right, pat yourself on the back. That means left is the negative direction for run.
A way to remember this is to think about the numbers are on the x -axis. Going to the right of the origin are the positive values, and going to the left of the origin are the negative values.
In other words, you will be going up and to the right OR down and to the left. The reason both negative directions work is our slope is rise over run and if you have a negative over a negative, it simplifies to be a positive.
If the slope is negative , then the rise and the run have to be opposites of each other, one has to be positive and one has to be negative.
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