Why does slope formula work

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. 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".

Using the example above, your population-growth model might be very accurate for the years through , but the city whose population is being measured might have been founded way back in What is the slope? This value tells me that, for every increase of 1 in my input variable t that is, for every increase of one year , the value of my output variable y will increase by 0.

The slope tells me that, every year, the average lifespan of American women increased by 0. The intercept value tells me that, in when they started counting , the average lifespan of an American woman was 73 years. So how do we find slope? The Slope Formula! Slope Formula Definition.

Example In the example to the right, we are asked to determine the slope of the line that passes through the ordered pairs -3,8 and 2, Then we substitute these numbers into the slope formula and calculate the slope.

Slope shows both steepness and direction. With positive slope the line moves upward when going from left to right. With negative slope the line moves down when going from left to right. The slope of a linear function is the same no matter where on the line it is measured. This is not true for non-linear functions.