56 CHAPTER 1 Graphs Chapter Review Things to Know Formulas Distance formula (p. 14) ( ) ( ) = − + − d x x y y 2 1 2 2 1 2 Midpoint formula (p. 16) ( ) ( ) = = + + M x y x x y y , 2 , 2 1 2 1 2 Slope (p. 33) = − − m y y x x 2 1 2 1 if ≠ x x ; 1 2 undefined if = x x 1 2 Parallel lines (p. 40) Equal slopes ( ) = m m 1 2 and different y-intercepts ( ) ≠ b b 1 2 Perpendicular lines (p. 42) Product of slopes is ( ) − ⋅ = − m m 1 1 1 2 ; slopes are negative reciprocals of each other = − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ m m 1 1 2 Equations of Lines and Circles Vertical line (p. 36) = x a; a is the x-intercept Horizontal line (p. 37) = y b; b is the y-intercept Point–slope form of the equation of a line (p. 36) ( ) − = − y y m x x m; 1 1 is the slope of the line, ( ) x y , 1 1 is a point on the line Slope–intercept form of the equation of a line (p. 37) = + y mx b m ; is the slope of the line, b is the y-intercept General form of the equation of a line (p. 39) + = Ax By C A B ; , not both 0 Standard form of the equation of a circle (p. 48) ( ) ( ) − + − = x h y k r ; 2 2 2 r is the radius of the circle, ( ) h k , is the center of the circle Equation of the unit circle (p. 49) + = x y 1 2 2 General form of the equation of a circle (p. 51) + + + + = x y ax by c 0 2 2 , with restrictions on a b , , and c Objectives Section You should be able to . . . Example(s) Review Exercises 1.1 1 Graph equations by plotting points (p. 4) 1–3 7–9 2 Graph equations using a graphing utility (p. 6) 4, 5 6, 7–9 3 Use a graphing utility to create tables (p. 8) 6 6 4 Find intercepts from a graph (p. 9) 7 5 5 Use a graphing utility to approximate intercepts (p. 9) 8 6 1.2 1 Use the distance formula (p. 13) 1–3 1(a)–4(a), 30(a), 32–34 2 Use the midpoint formula (p. 16) 4 1(b)–4(b), 33 1.3 1 Find intercepts algebraically from an equation (p. 20) 1 7–9 2 Test an equation for symmetry with respect to the x-axis, the y-axis, and the origin (p. 21) 2–6 10–14 3 Know how to graph key equations (p. 24) 7–9 15 1.4 1 Solve equations using a graphing utility (p. 29) 1–3 16, 17 1.5 1 Calculate and interpret the slope of a line (p. 32) 1 1(c)–4(c), 1(d)–4(d), 30(b), 31 2 Graph lines given a point and the slope (p. 35) 2 35 3 Find the equation of a vertical line (p. 36) 3 20 4 Use the point-slope form of a line; identify horizontal lines (p. 36) 4, 5 18–19 5 Use the slope-intercept form of a line (p. 37) 6 18, 19, 21–25
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