The slope of a line is well. the slope of it. To find it look at this example:
Are ordered pair is: (6,3) and (8,4)
a fast and simple way to do it is like this:
the formula is y sub 2-y sub 1 over x sub 2- x sub 1.
subrtract 3 from 4 which is equal to 1. subtract 6 from 8 which is equal to 2. Your answer is 1 over 2.
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If you have any expression that defines a line, you can find the slope of the line. After you have found the slope of the line, you can then write an expression describing the line in slope intercept form. You can't define a slope-intercept form for any nonlinear equation, because the slope is always* changing; there are often several intercepts as well.
The slope of a curved line at a point is the slope of the tangent to the curve at that point. If you know the equation of the curve and the curve is well behaved, you can find the derivative of the equation of the curve. The value of the derivative, at the point in question, is the slope of the curved line at that point.
The line perpendicular to a line with a slope of 1/5 has a slope of -5.
The slope of a line is undefined if the line is vertical.
The slope of a line perpendicular to one with slope m is -1/m. So for a line with slope 1/7, any line perpendicular to it will have: slope = -1 / (1/7) = -7