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# How do you find slopes?

Slope is easy. Just remember rise over run or change in y over change in x.

Pick two points on the line: (x1, y1) and (x2, y2)

The slope of the line is (y2-y1)/(x2-x1)

How to find the slope if you are given two points:

The equation for the slope of a line is (y2-y1)/(x2-x1). For example, if you have the points (4,8) and (7,6), the slope is (6-8)/(7-4), which is (-2)/3, which is -2/3. You can switch the x's and y's in the equation and get the same result, so you can rewrite the equation as (y1-y2)/(x1-x2). Using the points (4,8) and (7,6), the slope is (8-6)/(4-7), which is (2)/(-3), which is also -2/3.

If you end up with 0 on the bottom (such as 4/0), the slope is undefined (since the line goes straight up and down.)

How to find slope if you are given the equation of a line in slope-intercept form:

See the related question below, "How_do_you_find_the_slope_of_an_equation".

How to find slope if you are given the equation of a line in point-slope form:

See the related question below, "How_do_you_find_the_slope_of_an_equation".

How to find the slope if you are given the equation of a line in standard form:

See the related question below, "How_do_you_find_the_slope_of_an_equation".

How to find slope if you are given the graph of a line:

See the related question below, "How_do_you_find_slope_on_a_graph".

How to find the slope of a parallel or perpendicular line:

The slope of a line parallel to a line with at given slope is the same as the line with the given slope. For example, the slope of a line parallel to a line with a slope of 3/2 is 3/2, and the slope of a line parallel to a line with a slope of -5 is -5.

The slope of a line perpendicular to a line with a given slope is the negative reciprocal of the slope if the given line. Flip the bottom and top of the fraction, and then change the sign. For example, the slope of a line perpendicular to a line with a slope of 5/4 is -4/5. The slope of a line perpendicular to a line with a slope of 5 is -1/5. The slope of a line perpendicular to a line with a slope of -3/2 is 2/3. Study guides

a few ways, it is the change in y/change in x,

in a line equation y=mx+b slope =m (y=5x+7) slope =5

to see the change in y over x for this example try

x=1

(5)*1+7=y=12

x=2

5*2+7=17

change in y=5

change in x=1

slope=5

* * * * *

More generally, if y = f(x) is a [locally] differentiable function, its slope at x = x0 is

dy/dx evaluated at x0. Just below the hills.  Earn +20 pts  