Parallel and Perpendicular Lines Slopes and Equations of Lines

Slopes of Lines • Def: The slope of a line is the ratio of the vertical rise to it’s horizontal run. • The slope can also be used to describe a rate of change.

Considerations about two lines Parallel, perpendicular or neither • Parallel: Share the same Slope • Perpendicular: the product of the slopes is -1. • Neither: Neither parallel perpendicular. • Horizontal and vertical lines.

Positive and negative slopes

Ways to find the slope • Two points are given – Use equation • Graph is given – Observe the change

Equations of Lines Review • Can be written given: – The Slope and y intercept – The Slope and the coordinates of a point on the line. – The coordinates of two points of the line.

Slope and y-intercept • m: Slope of the line • b: y-intercept Write the equation of a line with a slope of (-4) and a y-intercept of 1.

Point, Slope form • The Slope and a point are given • EG: Write an equation of the line whose slope is -1/2 and contains (3, -7)

Two Points • write the equation for a line that contains (4, -1) and (-2, -1)

Two Points • write the equation for a line that contains ( -4, -2) and (2, 8) • Now draw a perpendicular to it that passes through (3, -2)

Homework • Page 143: Problems 25 to 37 odd • Pages 148 and 149: Problems 13 to 45 odd. • Compare your answers to the guide in the back of the book.