1-31-13Unit 1 Basics of Geometry

Review of Formulas

Formula for Slope m y2 y1x2 x1

Ax By C

ymx b

y y1 m x x1

Standard Form

Slope-intercept Form

Point-Slope Form

*where A>0 and A, B, C are integers

Write the equation of a line that passes through a given point, parallel to a given line.Write the equation of a line that passes through a given point, perpendicular to a given line.

Parallel lines have the same slopes.

3

1m

3

1m

Lines in the same plane that do not intersect are called parallel lines. Parallel lines have the same slope.

Parallel lines

Perpendicular lines have opposite reciprocal slopes. In order to find the slope of a line perpendicular to a given line, simply find the slope of the given line, take its reciprocal (flip it over) and make it the opposite sign .

3

1m

31

3m

Perpendicular LinesLines that intersect at

right angles are called perpendicular lines. The slopes of these lines are opposite reciprocals.

From the given equations, determine if the corresponding lines are parallel, perpendicular, or neither.

15

25

1

xy

xy

y = 2x + 2y = 4x - 2

2x + 6y = 14x + 12y =3

neither

perpendicular

parallel

Example 1: Write the slope intercept form of an equation for the line that passes through (12,3), and is parallel to the graph of

53

4 xy

Example 2:Write the slope intercept form of an equation for the line that passes through (1, -3), and is perpendicular to the graph of

42

1 xy

Example 3:Write the slope intercept form of an equation for the line that passes through (-6, 5), and is perpendicular to the graph of x - y= 5