The unemployment-rate graph in Figure 4, below, illustrates a common pattern of many line graphs: some segments where the slope is positive, other segments where the slope is negative, and still other segments where the slope is close to zero. The slope of a straight line between two points can be calculated in numerical terms. The rise is 2 units. It is positive as you moved up. Count the number of units. The run is 4 units.
It is positive as you moved to the right. Practice until you feel comfortable doing the questions and then move on. Graphs of economic relationships are not always straight lines. In this course, you will often see nonlinear curved lines, like Figure 6, which shows the relationship between quantity of output being produced and the cost of producing that output. As the quantity of output increases, the total cost increases at a faster rate. Table 1 shows the data behind this graph. Figure 6. In this example, the total cost of production increase at a faster rate when the quantity of output increases.
We can interpret nonlinear relationships similarly to the way we interpret linear relationships. Their slopes can be positive or negative.
So change in y is equal to negative one. So our change in y over our change in x is equal to negative one over one which is equal to negative one. So the slope of this line is negative one. Now if you had a slope with negative two, it would decrease even faster. So a line with a slope of negative two could look something like this.
So as x increases by one, y would decrease by two. So it would look something like Notice, as our x increases by a certain amount, our y decreases by twice as much. So this right over here has a slope of negative two. So hopefully this gives you a little bit more intuition for what slope represents and how the number that we use to represent slope, how you can use that to visualize how steep a line is.
A very high positive slope, as x increases, y is going to increase fairly dramatically. If you have a negative slope And then the higher the slope, the steeper, the more you increase as x increases, and the more negative the slope, the more you decrease as x increases. Intro to slope. Here are some visuals to help you with this definition:. Note that when a line has a positive slope it goes up left to right. Note that when a line has a negative slope it goes down left to right.
Given two points and. Note that we use the letter m to represent slope. Example 1 : Find the slope of the straight line that passes through -5, 2 and 4, This form can be handy if you need to find the slope of a line given the equation.
In this form, the slope is m , which is the number in front of x. In our problem, that would have to be In this form, the y -intercept is b , which is the constant. In our problem, that would be 2. We can get down to business and answer our question of what are the slope and y -intercept. In our problem, that would have to be 2. In our problem, that would be Looking at the graph, you can see that this graph never crosses the y -axis, therefore there is no y -intercept either.
Another way to look at this is the x value has to be 0 when looking for the y -intercept and in this problem x is always 5. So, for all our efforts on this problem, we find that the slope is undefined and the y -intercept does not exist. Looking at the graph, you can see that this graph crosses the y -axis at 0, So the y-intercept is 0, The slope is 0 and the y -intercept is Note that two lines are parallel if there slopes are equal and they have different y -intercepts.
What do you think? The slope of the first equation is 7 and the slope of the second equation is 7. Since the two slopes are equal and their y -intercepts are different, the two lines would have to be parallel. Is it going up from left to right or is it going down from left to right?
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