8.2 Graphing Linear Equations

Equations of Lines in the Coordinate PlaneSection 3.7 p.189Graphing Linear EquationsDefinitions:

Cartesian Coordinate Plane a graph

X axis the horizontal axis of a coordinate plane

Y axis the vertical axis of a coordinate planeGraphing Linear EquationsDefinitions:Origin where the two axes meet (0,0)Ordered pair x and y values of a point on a graphAlso called a point of a set of coordinatesQuadrants the four sections that the x and y axes divide the coordinate plane into named I, II, III, and IVCoordinate PlaneIdentifyOriginY-axisX-axisQuadrants I, II, III, and IV

Rise Up Run OutSlopeSteepnessWhat are some examples where slope is a factor?grade of a road, incline of wheelchair ramp, pitch of a roof, etc.

Slope of a LineDetermine the slope of a line given the coordinates of two points on the line

Find the slope of the segment below(5, 4) and (3, -1)

Slope =

m= =

Positive vs. negative slope

Positive slope- rises to the rightNegative slope- falls to the right

SlopeHorizontal lineSlope = y = 0 = 0xx

Vertical lineSlope = y = y = undefinedx 0

Slope of a LineSpecial cases:

x = 4What will this slope be?

y = - 3 What will this slope be?Slope-Intercept Form

Point-Slope FormMore PracticeHomeworkP.194-195 #9-41 odd

Additional Practice13-2 Slope of a Line worksheetHow do you think the slopes of parallel lines compare?

What about perpendicular lines?Slopes of Parallel Lines (GSP)

Slopes of Perpendicular Lines (GSP)

Two non-vertical lines are parallel if and only if their slopes are equal.(parallel lines have the same slope)

Two non-vertical lines are perpendicular if and only if the product of their slopes is -1(slopes of perpendicular lines are negative reciprocals of each other)m1 *m2 = -1 or m1= -1/m23.8 Slopes of Parallel and Perpendicular LinesGiven a line through points (5,-1) and (-3, 3), find the slope of all linesA. parallel to this oneB. perpendicular to this one

Slope = (-1 3)/ (5 (-3)) = -4/8 = -1/2A. slope = -1/2B. slope = 2Are the two lines below perpendicular?(-4, 2) and (0, -4)(-5, -3) and (4, 3)

Homeworkp.201-203 #7-10, 15-18, 23, 25, 31, 3313-3 Parallel and Perpendicular Lines worksheet13-7 Writing Linear Equations worksheet #11-23 odd, 24-26 all

Find the distance between points A and B

ABTwo points in a horizontal lineDistance = absolute value of the difference in the x-coordinatesDistance=|-2 2| = 4 or |2 (-2)| = 4Find the distance between points A and B

ABTwo points in a vertical lineDistance = absolute value of the difference in the y-coordinatesDistance=|-8 3| = 11 or |3 (-8)| = 11What about two points that do not lie on a horizontal or vertical line?How can you find the distance between the points?

The distance between two points is equal to the length of the segment with those points as the endpointsThe Distance FormulaThe distance between points (x1, y1) and (x2, y2) is given by:

d =

Find the distance between (0, 0) and (7, 24)d =d = 25

Midpoint Formula ReviewClass work13-1 Distance Formula worksheet 13-5 Midpoint Formula worksheet