Geometry

Solutions

Problem Set #3

Part One

 

Develop the equation of the straight line meeting the given conditions and put it into slope-intercept form  (y = mx + b)

 

  1. it passes through  (2,-1)  and  (-4,17)   y = -6x + 11
  2. it satisfies   8x + 4y + 9 = 0     y = -2x -9/4
  3. it has a slope of  -2 and passes through  (2,4)  y = -2x + 8
  4. it is perpendicular  to  3x + 9y = 12  and passes through  (1,4)  y = 3x + 1
  5. it is horizontal and passes through  (2,-3)    y= -3
  6. it goes through  (3,2),  (5,8)   and  (9,20)    y = 3x - 7
  7. it increases at a 45 degree angle to the positive x axis and passes through (4,0)  y = x -4
  8. it is tangent to the circle  x2 + y2 = 25  at the point     y = -x + 10/√2   or  y = -x +5√2
  9. it goes down 6 units for every 3 units it goes to the right and passes through (3,1)   y= -2x + 7
  10. it has a slope of -2 and passes through the point  (4,1)  y = -2x +9

 

 

Part Two – graphs involving straight lines – sketch each carefully and neatly

 

  1. The point  (2, 1 )  is on the parabola  y=x2/4  The tangent line to the parabola at that point has slope of 1.  Sketch both the parabola and the tangent line and write down the equation of the line as well.   y = x -1  is the tangent line

 

 

  1. Sketch the line and circle from Part One, #8  

 

 

 

  1.  The parabola  y = -x2  + 9  has a tangent line with slope of -2  at the place where x = 1.  Sketch both the parabola and tangent line

The tangent line is  y = -2x +10  and passes through the point  (1,8)

 

 

 

 

  1. Sketch the line whose equation is  3x + 9y =  24 by finding its x and y intercepts first.

                                       The intercepts  at at  (0,24/9)    and  (8,0)  on the y and x axes , respectively.