Because the line slopes downwards to the right, it has a negative slope. As x increases, y decreases. If the line sloped upwards to the right, the slope would be a positive number. Adjust the points above to create a positive slope. A way to remember this method is "rise over run". It is the "rise" - the up and down difference between the points, over the "run" - the horizontal run between them.
Just remember that rise going downwards is negative. Positive slope Here, y increases as x increases, so the line slopes upwards to the right. The slope will be a positive number. Negative slope Here, y decreases as x increases, so the line slopes downwards to the right. The slope will be a negative number.
The line on the right has a slope of about Zero slope Here, y does not change as x increases, so the line in exactly horizontal.
Graphing from this format can be quite straightforward, particularly if the values of " m " and " b " are relatively simple numbers — such as 2 or —4. In this lesson, we are going to look at the "real world" meanings that the slope and the y -intercept of a line can have, in context.
In other words, given a "word problem" modelling something in the real world, or an actual real-world linear model, what do the slope and intercept of the modelling equation stand for, in practical terms? Back when we were first graphing straight lines, we saw that the slope of a given line measures how much the value of y changes for every so much that the value of x changes.
For instance, consider this line:. This means that, starting at any point on this line, we can get to another point on the line by going up 3 units and then going to the right 5 units. But and this is the useful thing we could also view this slope as a fraction over 1 ; namely:. This tells us, in practical terms, that, for every one unit that the x -variable increases that is, moves over to the right , the y -variable increases that is, goes up by three-fifths of a unit.
While this doesn't necessarily graph as easily as "three up and five over", it can be a more useful way of viewing things when we're doing word problems or considering real-world models. Slope: Very often, linear-equation word problems deal with changes over the course of time; the equations will deal with how much something represented by the value on the vertical axis changes as time represented on the horizontal axis passes. An exercise might, say, talk about how the population grows, year on year, in a certain city, assuming that the population increases by a certain fixed amount every year.
For every year that passes that is, for every increase of 1 along the horizontal axis , the population would increase that is, move up along the vertical axis by that fixed amount.
For a time-based exercise, this will be the value when you started taking your reading or when you started tracking the time and its related changes. In the example from above, the y -intercept would be the population when the sociologists started keeping track of the population. Advisory: "When you started keeping track" is not the same as "when whatever it is that you're measuring started".
Great story! Good for you and the student for being honest about your findings as opposed to pretending to some settled answer. I had never thought of this. I will now never stop thinking about this. Damn you, man! Monday, December 14, Why m for Slope? Question: Why do we use m for the slope of a line? Michael Sullivan's College Algebra 8th Ed. Investigate the origin of this symbolism. Begin by consulting a French dictionary and looking up the French word monter.
Write a brief essay on your findings. Of course, "monter" is a French verb which means "to climb" or "to go up". But others disagree.
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