2-4 More About Linear Equations

Objective

To write an equation of a line given its slope and a point on the line

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If you travel along a line that is parallel to a given line, you will stay the same distance from the given line. If you travel along a line that is perpendicular to a given line, you will travel either toward or away from the given line along the most direct path.

Essential Understanding The slopes of two lines in the same plane indicate how the lines are related.

Given the slope and y-intercept, you can write the equation of a line in slope-intercept form. You can also write the equation of a line in point-slope form.

Here's Why It Works By substituting the general point (x, y), for ( x 2 , y 2 ) open , x sub 2 , comma , y sub 2 , close  in the slope formula, you can rewrite the slope formula in point-slope form.

m = y 2 − y 1 x 2 − x 1 = y − y 1 x − x 1 m ( x − x 1 ) = y − y 1 x − x 1 ( x − x 1 ) m ( x − x 1 ) = y − y 1 y − y 1 = m ( x − x 1 ) table with 4 rows and 2 columns , row1 column 1 , m , column 2 equals . fraction y sub 2 , minus , y sub 1 , over x sub 2 , minus , x sub 1 end fraction . equals . fraction y minus , y sub 1 , over x minus , x sub 1 end fraction , row2 column 1 , m . open . x minus , x sub 1 . close , column 2 equals . fraction y minus , y sub 1 , over x minus , x sub 1 end fraction . open . x minus , x sub 1 . close , row3 column 1 , m . open . x minus , x sub 1 . close , column 2 equals y minus , y sub 1 , row4 column 1 , y minus , y sub 1 , column 2 equals m . open . x minus , x sub 1 . close , end table

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