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Question

A)find the x-intercept and y-intercept of the line described by each equation
1. 6x-5y=11
2. y=-4x+5
B) find the slope intercept form of an equation for each graph described
1. slope -2, passes through (3,-1)
2. passes through (-4,7) and (-9,-1)
3. passes though (1,4) and is parallel to a line whose equation is y=3x+5
4. passes though (0,5) and is perpendicular to the line whose equation is y=6x-4
C) For each pair of equation, determine if the lines are parallel, perpendicular or either
1. y-3x=10 and 3y+x=-5
2. 5x-2y=10 and 2y+x=5

Answer 1

A) 

1. 6x -5y = 11

To find x intercept substitute y=0

6x - 5(0)=11

6x = 11

6x/6 =11/6

x=11/6

To find y intercept substitute x=0

6(0)-5y=11

-5y = 11

-5y/-5 =11/-5

y=-11/5

The x and y intercepts are x= 11/6 and y = -11/5

2.  y=-4x+5

To find x intercept substitute y=0

0= -4x+5

0 - 5 = -4x + 5 - 5

-5 = -4x

-5/-4 = -4x/-4

5/4 = x

To find y intercept substitute x=0

y = -4(0)+5

y = 5 

The x and y intercepts are x= 5/4 and y = 5

 

Answer 2

B)

1.   The slope intercept form is y = mx + b  

The equation of line  having slope m and passes through (x1,y1) is        ( y - y1) = m( x-x1)

So, the equation of line having slope -2 and passes through (3,-1) is    (y - (-1)) = -2( x-3)

y+1 = -2x +6

y+1-1 = -2x +6 -1

y = -2x +5

the slope intercept form is y = -2x +5

2.

 Consider (x1,y1) = (-4,7) and (x2,y2) = (-9,-1)

 Here m=(y2-y1)/(x2-x1)

 m = (-1-7)/-9-(-4)

 m= -8/-9+4 = -8/-5 = 8/5

The line equation is   (y - 7) = 8/5 ( x -(-4))

                                  5(y - 7)= 8(x + 4)

                                  5y - 35 = 8x +32

                                  5y - 35 +35 = 8x +32 +35

                                  5y =8x +67

                                  y = (8/5)x +67/5

The slope intercept form is y = (8/5)x +67/5

Answer 3

B)

3.  Here the required line parallel to y=3x+5

     If two lines are parallel then their slopes are equal

    So, the required line has slope m = 3

    The equation of line passes through (1,4) and has slope 3 is   (y - 4) = 3( x -1)

                                                                                                          y - 4 = 3x - 3

                                                                                                          y - 4 + 4 = 3x - 3 + 4

                                                                                                          y = 3x +1

                                                      The slope intercept form is      y = 3x +1

4.

Here the required line perpendicular to y=6x-4

If two lines are perpendicular  then their slopes are opposite reciprocals

So, the required line has slope m = -1/6

The equation of line passes through (0,5) and has slope  -1/6 is   (y - 5) = -1/6( x -0)

                                                                                                                 y - 5 = -(1/6)x

                                                                                                                y = -(1/6)x + 5

                                                            The slope intercept form is     y = -(1/6)x + 5

                                                                                    

Answer 4

C)

1.

    If two lines are parallel then their slopes are equal

    If two lines are perpendicular  then their slopes are opposite reciprocals

    Now find slopes of  y - 3x=10 and 3y+x=-5

    y - 3x=10

    y = 3x + 10   here slope  m = 3

   3y + x = -5

   3y = -x -5

    y = -(1/3)x -5/3 her slope m= -1/3

   Since the two slopes are opposite recipracals.

   So, the two lines are perpendicular.

 

2.

     If two lines are parallel then their slopes are equal

     If two lines are perpendicular  then their slopes are opposite reciprocals

     Now find slopes of 5x-2y=10 and 2y+x=5

    5x-2y=10

    5x-2y + 2y =10 +2y

    5x = 10 +2y

    5x -10 = 2y

    y = (5/2)x - 5         here slope m = 5/2

    2y + x= 5

    2y = -x +5

    y = -(1/2)x +5/2   here slope m = -1/2

    Here the two slopes are neither equal nor opposite reciprocal.

   So, the two lines are neither parallel nor perpendicular.