Editing Slope (section)

==Algebra and geometry==
[[File:Slopes of Parallel and Perpendicular Lines.svg|thumb|Slopes of parallel and perpendicular lines]]
{{bulleted list
| If <math>y</math> is a [[linear function]] of <math>x</math>, then the coefficient of <math>x</math> is the slope of the line created by plotting the function. Therefore, if the equation of the line is given in the form
: <math>y = mx + b</math>
then <math>m</math> is the slope. This form of a line's equation is called the ''slope-intercept form'', because <math>b</math> can be interpreted as the [[y-intercept]] of the line, that is, the <math>y</math>-coordinate where the line intersects the <math>y</math>-axis.
| If the slope <math>m</math> of a line and a point <math>(x_1, y_1)</math> on the line are both known, then the equation of the line can be found using the [[Linear equation#Point–slope form|point-slope formula]]:
: <math>y - y_1 = m(x - x_1).</math>
| The slope of the line defined by the [[linear equation]]
: <math>ax + by + c = 0 </math>  
is
: <math>-\frac{a}{b}</math>.
| Two lines are [[parallel (geometry)|parallel]] if and only if they are not the same line (coincident) and either their slopes are equal or they both are vertical and therefore both have undefined slopes. 
| Two lines are [[perpendicular]] if the product of their slopes is&nbsp;−1 or one has a slope of 0 (a horizontal line) and the other has an undefined slope (a vertical line).
| The angle θ between −90° and 90° that a line makes with the ''x''-axis is related to the slope ''m'' as follows:
: <math>m = \tan(\theta)</math>  
and 
: <math>\theta = \arctan (m)</math> &nbsp; (this is the inverse function of tangent; see [[inverse trigonometric functions]]).
}}

===Examples===
For example, consider a line running through points (2,8) and (3,20). This line has a slope, {{math|''m''}}, of 
: <math>\frac {(20 - 8)}{(3 - 2)} = 12. </math>

One can then write the line's equation, in point-slope form:
: <math>y - 8 = 12(x - 2) = 12x - 24. </math>
or: 
: <math>y = 12x - 16. </math>

The angle θ between −90° and 90° that this line makes with the {{math|''x''}}-axis is 
:<math>\theta = \arctan(12) \approx 85.2^{\circ} .</math>

Consider the two lines: {{math|1=''y'' = −3''x'' + 1}} and {{math|1=''y'' = −3''x'' − 2}}. Both lines have slope {{math|1=''m'' = −3}}. They are not the same line. So they are parallel lines.

Consider the two lines  {{math|1=''y'' = −3''x'' + 1}} and {{math|1=''y'' = {{sfrac|''x''|3}} − 2}}. The slope of the first line is {{math|1=''m''<sub>1</sub> = −3}}. The slope of the second line is {{math|1=''m''<sub>2</sub> = {{sfrac|1|3}}}}. The product of these two slopes is −1. So these two lines are perpendicular.