Lesson 3 – 3 Slopes of Lines Geometry Lesson 3 – 3 Slopes of Lines Objective: Find slope of lines. Use slope to identify parallel and perpendicular lines.

Slope

Find the slope 4 5 -6 3

Find the slope = 0 undefined

Slope Positive Slope Negative Slope Zero Slope Undefined Slope

Rate of Change Rate of change describes how a quantity y changes in relationship to quantity x. Fancy word for slope in word problems.

A pilot flies a plane from Columbus, Ohio, to Orlando, Florida. After 0.5 hour, the plane reaches its cruising altitude and is 620 miles from Orlando. Half an hour later, the plane is 450 miles from Orlando. How far was the plane from Orlando 1.25 hours after take off.

(0.5, 620), (1, 450) Need to write an equation for the info. A pilot flies a plane from Columbus, Ohio, to Orlando, Florida. After 0.5 hour, the plane reaches its cruising altitude and is 620 miles from Orlando. Half an hour later, the plane is 450 miles from Orlando. How far was the plane from Orlando 1.25 hours after take off. Need to write an equation for the info. Can you identify 2 points? (0.5, 620), (1, 450) Cannot have a decimal or fraction in a fraction. = -340 = - 340 mph Or 340 mph decrease Cont…

450 = -340(1) + b y = -340x + 790 Slope-Intercept form: y = mx + b A pilot flies a plane from Columbus, Ohio, to Orlando, Florida. After 0.5 hour, the plane reaches its cruising altitude and is 620 miles from Orlando. Half an hour later, the plane is 450 miles from Orlando. How far was the plane from Orlando 1.25 hours after take off. Slope-Intercept form: y = mx + b Plug in either point and slope to find b. 450 = -340(1) + b 450 = -340 + b 790 = b y = -340x + 790 How far was the plane from Orlando 1.25 hours after take off? y = -340(1.25) + 790 = -425 + 790 = 365 miles

Slope: Parallel and Perpendicular Lines Slopes of Parallel Lines Two nonvertical lines have the same slope if and only if they are parallel. All vertical lines are parallel. Slopes of Perpendicular Lines Two nonvertical lines are perpendicular if and only if the product of their slopes are –1. Vertical and horizontal lines are perpendicular. Slopes are opposite reciprocals.

Determine whether AB and CD are parallel, perpendicular, or neither. A (14, 13) B (-11, 0) C (-3, 7) D (-4, -5) Need to have both Slopes and answer Neither

Determine whether AB and CD are parallel, perpendicular, or neither. A (3, 6) B (-9, 2) C (5, 4) D (2, 3) Parallel

Determine whether AB and CD are parallel, perpendicular, or neither. A (1,1) B (-1, -5) C (3, 2) D (6, 1) Perpendicular

Graph the line that contains A (-3, 0) and is perpendicular to CD with C (-2, -3) and D (2, 0) So a line AB perpendicular to line CD would have a slope of what?

Homework Pg. 190 1 – 11 all, 12 – 48 EOE