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1. Solve P = 2L + 2W for L 2. Solve A = 1/2 bh for h

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1 1. Solve P = 2L + 2W for L 2. Solve A = 1/2 bh for h
Quiz 1. Solve P = 2L + 2W for L 2. Solve A = 1/2 bh for h 3. A chemist must mix 8 L of a 40% solution with 70% solution to get a 50% solution. How much of the 70% solution should be used?

2 Ten liters of a 4% acid solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

3 Slope of a Line

6 Slope An important characteristic of a straight line is its slope, a numerical measure of the steepness of the line. (Geometrically, this may be interpreted as the ratio of rise to run.

7 Find the slope of the line through each of the following pairs of points.
y x

8 Find the slope of the line through each of the following pairs of points.
y x

9 Find the slope of the line through each of the following pairs of points.
y x

10 Find the slope of the line through each of the following pairs of points.
y x

11 Find the slope of the line through each of the following pairs of points.
y x

12 Find the slope of the line through each of the following pairs of points.
y x

13 Find the slope of the line through each of the following pairs of points.
y x

14 Find the slope of the line through each of the following pairs of points.
y x

15 Find the slope of the line through each of the following pairs of points.
y x

16 Find the slope of the line through each of the following pairs of points.
y x

17 Find the slope of the line through each of the following pairs of points.
y x

18 Find the slope of the line through each of the following pairs of points.
y x

19 Find the slope of the line through each of the following pairs of points.
y x

20 Find the slope of the line through each of the following pairs of points.
y x

21 Find the slope of the line through each of the following pairs of points.
y x

22 Find the slope of the line through each of the following pairs of points.
y x

23 Find the slope of the line through each of the following pairs of points.
y x

24 Find the slope of the line through each of the following pairs of points.
y x

25 Find the slope of the line through each of the following pairs of points.
y x

26 Find the slope of the line through each of the following pairs of points.
y x

27 Find the slope of the line through each of the following pairs of points.
y x

28 Find the slope of the line through each of the following pairs of points.
y x

29 Find the slope of the line through each of the following pairs of points.
y x

30 Find the slope of the line through each of the following pairs of points.
y x

31 Find the slope of the line through each of the following pairs of points.
y x

32 Find the slope of the line through each of the following pairs of points.
y x

33 Find the slope of the line through each of the following pairs of points.
y x

34 Find the slope of the line through each of the following pairs of points.
y x

35 Find the slope of the line through each of the following pairs of points.
y x

36 Find the slope of the line through each of the following pairs of points.
y x

37 Find the slope of the line through each of the following pairs of points.
y x

38 Find the slope of the line through each of the following pairs of points.
y x

39 Find the slope of the line through each of the following pairs of points.
y x

40 Find the slope of the line through each of the following pairs of points.
y x

41 Find the slope of the line through each of the following pairs of points.
y x

42 Find the slope of the line through each of the following pairs of points.
y x

43 Find the slope of the line through each of the following pairs of points.
y x

44 Find the slope of the line through each of the following pairs of points.
y x

45 Find the slope of the line through each of the following pairs of points.
y x

46 Find the slope of the line through each of the following pairs of points.
y x

47 Find the slope of the line through each of the following pairs of points.
y x

48 Find the slope of the line through each of the following pairs of points.
y x

49 Find the slope of the line through each of the following pairs of points.
y x

50 Find the slope of the line through each of the following pairs of points.
y x

51 Find the slope of the line through each of the following pairs of points.
y x

52 Find the slope of the line through each of the following pairs of points.
y x

53 Find the slope of the line through each of the following pairs of points.
y x

54 Find the slope of the line through each of the following pairs of points.
y x

55 The difference x2-x1 is called the change in x
The difference y2-y1 is called the change in y 8 6 (x2,y2) 4 (x1,y1) 2 (x2,y1) -2 2 4 6

56 Slope Using Coordinates
The slope m of the line through the points (x1,y1) and (x2,y2) is

57 Slope Using Coordinates
The slope m of the line through the points (x1,y1) and (x2,y2) is m = = rise y2 - y1 run x2 - x1

58 Slope Using Coordinates
The slope m of the line through the points (x1,y1) and (x2,y2) is m = = rise y2 - y1 run x2 - x1 Note: when x2 - x1 = 0 then the line line is vertical and the slope is undefined

59 Find the slope of the line
y x

60 Find the slope of the line
y x

61 Find the slope of the line
y x

62 Find the slope of the line
y x

63 Find the slope of the line
y x

64 Find the slope of the line
y x

65 Find the slope of the line
y x

66 Find the slope of the line
y x

67 Find the slope of the line
y x

68 Find the slope of the line
y x

69 Find the slope of the line
y x

70 Find the slope of the line
y x

71 Find the slope of the line
y x

72 Find the slope of the line
y x

73 Find the slope of the line
y x

74 Find the slope of the line
y x

75 Find the slope of the line
y x

76 Find the slope of the line
y x

77 Find the slope of the line
y x

78 Find the slope of the line
y x

79 Find the slope of the line
y x

80 Find the slope of the line
y x

81 Find the slope of the line
y x

82 Find the slope of the line
y x

83 Find the slope of the line
y x

84 Find the slope of the line
y x

85 Find the slope of the line
y x

86 Find the slope of the line
y x

87 Find the slope of the line
y x

88 Find the slope of the line
y x

89 Find the slope of the line
y x

90 Slope

91 The slope of a horizontal line is 0

92 The slope of a horizontal line is 0
The slope of a vertical line is undefined..

93 The slope of a horizontal line is 0
The slope of a vertical line is undefined. Do not say that a vertical line has no slope because “no slope” could be confused with 0 slope, which is the slope of a horizontal line.

94 Solve for y to find the slope of the line

95 Solve for y to find the slope of the line

96 Solve for y to find the slope of the line

97 Solve for y to find the slope of the line

98 Solve for y to find the slope of the line

99 Solve for y to find the slope of the line

100 Solve for y to find the slope of the line

101 Solve for y to find the slope of the line

102 Solve for y to find the slope of the line

103 Solve for y to find the slope of the line

104 Solve for y to find the slope of the line

105 Solve for y to find the slope of the line
4x - y = -8

106 4x - y = -8 Standard Form Ax + By = C
Solve for y to find the slope of the line 4x - y = -8 Standard Form Ax + By = C

107 4x - y = -8 Standard Form Ax + By = C
Solve for y to find the slope of the line 4x - y = -8 Standard Form Ax + By = C

108 4x - y = -8 Standard Form Ax + By = C Slope Intercept Form
Solve for y to find the slope of the line 4x - y = -8 Standard Form Ax + By = C Slope Intercept Form

109 4x - y = -8 Standard Form Ax + By = C Slope Intercept Form y = 4x + 8
Solve for y to find the slope of the line 4x - y = -8 Standard Form Ax + By = C Slope Intercept Form y = 4x + 8

110 4x - y = -8 Standard Form Ax + By = C Slope Intercept Form y = 4x + 8
Solve for y to find the slope of the line 4x - y = -8 Standard Form Ax + By = C Slope Intercept Form y = 4x + 8 y = mx + b

111 Find the slope of the line
y x

112 Find the slope of the line
y x

113 Find the slope of the line
y x

114 Find the slope of the line
y x

115 Find the slope of the line
y x

116 Find the slope of the line
y x

117 Find the slope of the line
y x

118 Find the slope of the line
y x

119 Find the slope of the line
y x

120 Find the slope of the line
y x

121 Find the slope of the line
y x

122 Find the slope of the line
y x

123 Find the slope of the line
y x

124 Find the slope of the line
y x

125 Find the slope of the line
y x

126 Find the slope of the line
y x

127 Find the slope of the line
y x

128 Find the slope of the line
y x

129 Find the slope of the line
y x

130 Find the slope of the line
y x

131 Find the slope of the line
y x

132 Find the slope of the line

133 Find the slope of the line

134 Find the slope of the line

135 Find the slope of the line

136 Find the slope of the line

137 Find the slope of the line

138 Find the slope of the line

139 Find the slope of the line

140 Find the slope of the line

141 Find the slope of the line

142 Find the slope of the line

143 Find the slope of the line

144 Find the slope of the line

145 Find the slope of the line

146 Find the slope of the line

147 Find the slope of the line

148 Find the slope of the line

149 Find the slope of the line

150 Find the slope of the line

151 Find the slope of the line

152 Find the slope of the line

153 Find the slope of the line

154 Find the slope of the line

155 Find the slope of the line

156 Find the slope of the line

157 Graph the line with slope 2/3
passing through the point (-1,4) y x

158 Graph the line with slope 2/3
passing through the point (-1,4) y x

159 Graph the line with slope 2/3
passing through the point (-1,4) y x

160 Graph the line with slope 2/3
passing through the point (-1,4) y x

161 Graph the line with slope 2/3
passing through the point (-1,4) y x

162 Graph the line with slope 2/3
passing through the point (-1,4) y x

163 Graph the line with slope 2/3
passing through the point (-1,4) y x

164 Graph the line with slope 2/3
passing through the point (-1,4) y x

165 Graph the line with slope 2/3
passing through the point (-1,4) y x

166 Graph the line with slope 2/3
passing through the point (-1,4) y x

167 Graph the line with slope 2/3
passing through the point (-1,4) y x

168 Graph the line with slope 2/3
passing through the point (-1,4) y x

169 Graph the line with slope 2/3
passing through the point (-1,4) y x

170 Graph the line with slope 2/3
passing through the point (-1,4) y x

171 Graph the line with slope 2/3
passing through the point (-1,4) y x

172 Graph the line with slope 2/3
passing through the point (-1,4) y x

173 Graph the line with slope 2/3
passing through the point (-1,4) y x

174 Graph the line with slope -4 passing through
y the point (3,1) x

175 Graph the line with slope -4 passing through
y the point (3,1) x

176 Graph the line with slope -4 passing through
y the point (3,1) x

177 Graph the line with slope -4 passing through
y the point (3,1) x

178 Graph the line with slope -4 passing through
y the point (3,1) x

179 Graph the line with slope -4 passing through
y the point (3,1) x

180 Graph the line with slope -4 passing through
y the point (3,1) x

181 Graph the line with slope -4 passing through
y the point (3,1) x

182 Graph the line with slope -4 passing through
y the point (3,1) x

183 Graph the line with slope -4 passing through
y the point (3,1) x

184 Graph the line with slope -4 passing through
y the point (3,1) x

185 Graph the line with slope -4 passing through
y the point (3,1) x

186 Graph the line with slope -4 passing through
y the point (3,1) x

187 Graph the line with slope -4 passing through
y the point (3,1) x

188 Graph the line with slope -4 passing through
y the point (3,1) x

189 Graph the line with slope -4 passing through
y the point (3,1) x

190 Graph the line with slope -4 passing through
y the point (3,1) x

191 Graph the line with slope -4 passing through
y the point (3,1) x

192 Graph the line with slope -4 passing through
y the point (3,1) x

193

194 Lines that have positive slope point upward with the right hand.

195 Lines that have negative slope point upward with the left hand.

196 Two lines with slopes m1 and m2 are parallel if and only if
Parallel lines Two lines with slopes m1 and m2 are parallel if and only if

197 Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.

198 Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.

199 Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.

200 Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.

201 Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.

202 Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.

203 Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.

204 Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.

205 Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.

206 Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.

207 Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.

208 (-2,-3) & (5,-5) y x

209 (-2,-3) & (5,-5) y x

210 (-2,-3) & (5,-5) y x

211 (-2,-3) & (5,-5) y x

212 (-2,-3) & (5,-5) y through the origin x

213 (-2,-3) & (5,-5) y through the origin x

214 (-2,-3) & (5,-5) y through the origin x

215 (-2,-3) & (5,-5) y through the origin x

216 (-2,-3) & (5,-5) y through the origin x

217 (-2,-3) & (5,-5) y through the origin x

218 (-2,-3) & (5,-5) y through the origin x

219 (-2,-3) & (5,-5) y through the origin x

220 (-2,-3) & (5,-5) y through the origin x

221 (-2,-3) & (5,-5) y through the origin x

222 (-2,-3) & (5,-5) y through the origin x

223 (-2,-3) & (5,-5) y through the origin x

224 y One line has a slope of 2 Perpendicular lines x

225 y One line has a slope of 2 Perpendicular lines x

226 One line has a slope of 2 and the other line has a slope of -1/2
y One line has a slope of 2 and the other line has a slope of -1/2 Perpendicular lines x

227 One line has a slope of 2 and the other line has a slope of -1/2
y One line has a slope of 2 and the other line has a slope of -1/2 Perpendicular lines x

228 One line has a slope of 2 and the other line has a slope of -1/2
y One line has a slope of 2 and the other line has a slope of -1/2 Perpendicular lines x

229

230 Two lines with slopes m1 and m2 are perpendicular if and only if
Perpendicular lines Two lines with slopes m1 and m2 are perpendicular if and only if