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Chapter 2 Review Equations of Lines

This chapter includes a review of equations of lines, such as finding the domain and range, writing equations using slope-intercept and point-slope forms, graphing lines, and solving problems related to parallel and perpendicular lines. It also covers graphing functions and shifts on graphs.

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Chapter 2 Review Equations of Lines

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  1. Chapter 2 Review Equations of Lines 1. Give the domain and range: {(3,2) (5,1) (-4,2) (-3,0) (3,5)} D: {-4, -3, 3, 5}R: {0,1,2,5} Is it a function? NO – 3 goes to 2 and 5.

  2. Slope-intercept: y = mx + b 2. Write the equation of the line with slope -3 and y-intercept 4. Graph the line. y= -3x+4 y=-3x+4

  3. Point slope: y – y1 = m( x – x1) 3. Write the equation of the line that passes through (5,-2) and has slope of ⅔. Formula: y-y1 = m(x-x1) y+2 = ⅔(x-5) distribute y+2 = ⅔x-3⅓ Subtract 2 y = ⅔x-5⅓

  4. Point slope: y – y1 = m( x – x1) 4. Write the equation of the line that passes through (-1,4) and (-2,9) m = 9-4 -2+1 = -5 Formula: y-y1 = m(x-x1) y-4= -5(x+1) distribute y-4=-5x-5 add 4 y = -5x-1

  5. Point slope: y – y1 = m( x – x1) 5. Write the equation of the line parallel to y = 2x – 7 and passes (3,-2) m= 2 Formula: y-y1 = m(x-x1) y+2= 2(x-3) distribute y+2=2x-6 Subrtact 2 y = 2x-8

  6. 6. Write the equation of the line perpendicular to x + 4y = 8 and passes (-3,1) 4y = -x + 8y = -¼x + 2┴ slope is 4 Formula: y-y1 = m(x-x1) y-1= 4(x+3) distribute y-1=4x+12 Add 1 y = 4x+13

  7. WRITE IN STANDARD FORM:Ax + By = C 7. Write the equation of the line perpendicular to 2x – 3y = 6 and passes (2,-4) -3y = -2x + 6y = ⅔x - 2┴ slope is -3/2 y+4= -3/2(x-2)y + 4 = -3/2x + 3y = -3/2x - 1 ( ) 2 2y= -3x – 23x + 2y = -2

  8. Slope-intercept: y = mx + b 8. Graph the line: 5x – 2y = 8 -2y = -5x + 8 y = 5/2x - 4 y = 5/2x - 4

  9. 9. Graph the inequality: 2y > 3x - 8 y> 3/2 x - 4

  10. Piecewise function: If x > -2 If x ≤ -2 f(x)=

  11. 10. Graph the function: y = 3|x-4|+2 Describe the shifts: SHIFTS OF GRAPHS y = a|x| if a<1 get widery = a|x| if a>1 get narrowery = |x+h| moves left h unitsy = |x-h| moves right h unitsy = |x|+k moves up k unitsy = |x|-k moves down k units narrower by 3, up 2 and right 4

  12. 11. Graph the function: y = -2|x+1|-3 Describe the shifts: SHIFTS OF GRAPHS y = a|x| if a<1 get widery = a|x| if a>1 get narrowery = |x+h| moves left h unitsy = |x-h| moves right h unitsy = |x|+k moves up k unitsy = |x|-k moves down k units Reflects across the x axisnarrower by 2, down 3 and left 1.

  13. HOMEWORK Page 128 1-9 skip 6

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