Lines - Revision history

MathAdmin: /* Point Slope Form */

2016-03-27T21:07:12Z

Point Slope Form

MathAdmin: /* Slope intercept Form */

2016-03-27T21:06:48Z

Slope intercept Form

MathAdmin: /* Slope intercept Form */

2016-03-27T21:06:22Z

Slope intercept Form

MathAdmin: Created page with "
TOC
Lines, parallel, perpendicular, slope intercept, point-slope. ==Introduction== As was mentioned in the last section, lines are one of the..."

2015-10-05T17:53:59Z

Created page with "<div class="noautonum">__TOC__</div> Lines, parallel, perpendicular, slope intercept, point-slope. ==Introduction== As was mentioned in the last section, lines are one of the..."

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<div class="noautonum">__TOC__</div>

Lines, parallel, perpendicular, slope intercept, point-slope.
==Introduction==
As was mentioned in the last section, lines are one of the geometric object that requires the least amount of information to distinguish them. The only information we need is two points.
From this information we can find the slope of the line. From here we can determine if lines are two lines are parallel or perpendicular. Then there are two common ways to write the equation of a line.
These are called the slope intercept form and the point slope form.

==Slope, Parallel, Perpendicular==
As was mentioned before the first thing we will discuss is the slope of a line. Given two points, <math>(x_1, y_1) \text{ and }(x_2, y_2)</math> the formula for the slope is <math> \frac{y_2 - y_1}{x_2 - x_1}</math>.
From a geometric standpoint the slope tells you how quickly the line increases in y-value per each unit change in x-value.

Example: Find the slope of the line containing (5, 3) and (6, 9).

The slope, denoted m, is <math>\frac{9-3}{6-5} = 6 = \frac{3-9}{5-6}</math>.

Two lines <math> y = m_1 x + b_1 \text{ and } y = m_2 x + b_2</math> are parallel if <math> m_1 = m_2</math>

For example, y = 5x + 3 is parallel to y = 5x - 4, but is not parallel to y = -3x + 8.

Two lines, <math> y = m_1x +b_1 \text{ and } y = m_2x + b_2</math> are perpedicular if <math> m_1 = \frac{-1}{m_2}</math>.

For example, <math>y = 3x - 2</math> is perpendicular to <math> y = \frac{-1}{3}x + 5</math>, but is not parallel to <math> y = 3x + 5</math>

==Slope intercept Form==

The slope intercept form for a line provides us with both the slope, and y intercept without requiring any work. It also allows us to write the equation of a line with only two pieces of information, the slope and y-intercept.
Given a slope m, and y-intercept (0, b) the slope intercept form for the line is y = mx + b.

For example, Given a line with slope 5 and y-intercept (0, -2) the equation of the line, in slope intercept form, is y = 5x - 2.

==Point Slope Form==
The point slope form is a more widely applicable way to write the equation of a line. Just like the slope intercept form we only require knowledge of the slope, but we only need a point that is on the line, even if it is not the y-intercept.
Given a point <math>(x_1, y_1)</math> and a slope m, the point slope form for a line is <math> y - y_1 = m(x - x_1)</math>.

Example: Find the equation of a line with slope -2 going through the point (3, 7).

Solution: The equation for the line is <math> y - 7 = (-2)(x - 3)</math>

[[Math_5|'''Return to Topics Page]]

← Older revision		Revision as of 21:06, 27 March 2016
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	For example, Given a line with slope 5 and y-intercept (0, -2) the equation of the line, in slope intercept form, is y = 5x - 2.		For example, Given a line with slope 5 and y-intercept (0, -2) the equation of the line, in slope intercept form, is y = 5x - 2.
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	==Point Slope Form==		==Point Slope Form==

@@ Line 34: / Line 34: @@
 Given a point <math>(x_1, y_1)</math> and a slope m, the point slope form for a line is <math> y - y_1 = m(x - x_1)</math>.
-Example: Find the equation of a line with slope -2 going through the point (3, 7).
+'''Example:''' Find the equation of a line with slope -2 going through the point (3, 7).
-Solution: The equation for the line is <math> y - 7 = (-2)(x - 3)</math>
+'''Solution:''' The equation for the line is <math> y - 7 = (-2)(x - 3)</math>
 [[Math_5|'''Return to Topics Page]]

@@ Line 28: / Line 28: @@
 Given a slope m, and y-intercept (0, b) the slope intercept form for the line is y = mx + b.
-For example, Given a line with slope 5 and y-intercept (0, -2) the equation of the line, in slope intercept form, is y = 5x - 2.
+'''Example:''' Given a line with slope 5 and y-intercept (0, -2) the equation of the line, in slope intercept form, is y = 5x - 2.
 ==Point Slope Form==

Lines - Revision history

MathAdmin: /* Point Slope Form */

MathAdmin: /* Slope intercept Form */

MathAdmin: /* Slope intercept Form */

MathAdmin: Created page with "__TOC__ Lines, parallel, perpendicular, slope intercept, point-slope. ==Introduction== As was mentioned in the last section, lines are one of the..."

MathAdmin: Created page with "
TOC
Lines, parallel, perpendicular, slope intercept, point-slope. ==Introduction== As was mentioned in the last section, lines are one of the..."