To find the slope of a function in a graph, we find the slope, right?

Question

The m= y2-y1 / x2-x1..right? But my question is when we find the slope, what do we use that slope for in the graph. I don't really get this point. Can anyone plz explain more clearly for me?

Answer 1

You have the correct (one of several possible) formula for determining "slope".

Based on y=m*x+b (as a general linear formula), you are probably familiar with at least 2 of the values:

x : the "left-right" values of the formula, and
y : the "up-down", or vertical values of the formula,
given the coordinates in the form (x,y)

so what are b and m?

b is commonly refered to as the "y-Intercept" value.

Essentially, the coordinate (0,b) is where the linear equation, or line, crosses the y-axis.

And so we have the value of m......

m is referred to as the "slope" of the linear equation.

In the equation you have already noted, m is equal to the difference between 2 y values (from 2 coordinates on the line) divided by the difference between 2 x values (from the same 2 coordinates used before).

The first difference (y2-y1) is called the "rise" (referring to the difference in height).

The second difference (x2-x1) is called the "run" (referring to the horizontal difference )

so the slope (m) is equal to (=) the rise (y2-y1) divided by (/) the run (x2-x1).

You can use this to help you graph the equation now!

Simply count vertically by the amoutn of the rise, and horizontally by the amount of the run, making sure to start from an actual point on the line.

For example:

if you have a slope of 2, then you can say that is equal to 2/1 (2 divided by 1 is still "2").

So you would start at a given coordinate on your graph, and then simply count 2 up, and 1 across (going from left to right) from that point. This will be another point on your line!

If you continue to do this you will have a collection of points (coordinates) that represent various points of your equation.

I hope this helps you out!

Answer 2

If your graph is a straight line, then yes, you can find the slope for the function by taking m = (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2). The graph doesn't "use" the slope; the slope is just a characteristic of it. It tells you how fast the "rise" changes (the change in y) with the "run" (the change in x).

If the slope is very small, the line will be closer to horizontal. If the slope is large, the line will be closer to vertical. A positive slope means the line is stretching from the lower left to the upper right, while a negative slope indicates a line stretching from the top left to the bottom right. You'll find that the slope is the same no matter which two points you pick. And if you write the line in the form of y = mx + b, then m is the slope.

Answer 3

i agree with the other guys and would like to add that when you have the slope and graph of the line you can predict what y will be by looking at the x-intercept on the graph without having to always work out the function, and also vice versa. you can figure out the function by knowing the slope and y-intercepts to figure out the function for a certain problem.

graphs started making alot more sense when i got into statistics and saw the relationships between x and y intercepts. these slope problems are practice for getting into more involved stuff.
hope that helped a little.

Answer 4

something of the type y=mx+c (on your case f(x) is y, the notation y is often used to demote the actual actuality that is on the y axis) is a instantly line the position c is the intercept. So it is a instantly line, intercepting the y axis at a million and the slope is two. So at the same time as x=2, f(x)=5, x=3 then f(x)=7 etc. you'll discover how that is basic to comic strip.

Answer 5

when you plot a point on the graph. Then you use the slope. For example you graph the point (2,3) and your slope=5/3, so from that point you rise positive five on the y-intercept and run 3 on the x-intercept.

Answer 6

slope helps us quantify steepness.
The slope tells us whether the line goes up or down.
It tells us if it is flat or steep

m = rise / run ===> so you know how to get from one point on the curve to another, you go up "rise" and over "run"
connect these points.

example if slope is 3/4. We go up +three over +four

=)
hope that helps.
hard to do without pix.

Positive slope => means line goes up from left to right
negative slope means line goes down from left to right
slope of zero means horizontal line
small IslopeI<1 means flat
large IslopeI>1 means steep
vertical line has slope undefined (cannot run zero, it is division byzero)


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Answer 7

If finding the slope is an end in itself, you are correct. Often this is a part of a more intricate problem.

Answer 8

you have to find the slope(gradient) to be substituded into the general eq. of graph function, y=mx+c,so you could find the value of y.To build an eq.,you have to know the gradient and the passing through point.And you may find the gradient from the given coordinate and other information.

y=mx+c

m=gradient
c=y-intercept

Answer 9

yes you do. for example m= 5-1/6-3, your answer would be 4 over 3. 4= rise, 3=run. Hope this helps in anyway.