The formula y=mx+b

Question

Consider the line 6x+8y=-7

 

Find the equation of the line that is perpendicular to this line and passes through the point (-5,6)
Find the equation of the line that is parallel to this line and passes through the point (-5,6)

Find the equation of the line that is perpendicular to this line and passes through the point (-5,6)

Answer 1

Consider the line 6x + 8y = -7

Find the equation of the line that is perpendicular to this line and passes through the point (-5,6)
Find the equation of the line that is parallel to this line and passes through the point (-5,6)
Find the equation of the line that is perpendicular to this line and passes through the point (-5,6)

 

• First convert the equation to slope intercept form y = mx + b

6x + 8y = -7

6x + 8y - 6x = -6x - 7

8y = -6x - 7

8y/8 = -6x/8 - 7/8

y = (-3/4)x - 7/8

• The slope of this line is -3/4
• For a line perpendicular to y = (-3/4)x - 7/8 the slope must be the negative inverse, or 4/3

y = (4/3)x + b

• Now we have to solve for b (the y intercept)

6 = (4/3)(-5) + b

6 = -20/3 + b

6(3/3) + 20/3 = -20/3 + b + 20/3

18/3 + 20/3 = b

b = 38/3

• Now we have the line perpendicular to 6x + 8y = -7 that passes through the point (-5,6)

y = (4/3)x + 38/3

• Now to find the line that is parallel to 6x + 8y = -7 and passes through the point (-5,6)
• To be parallel it will have the same slope, but a different y intercept

y = (-3/4)x + b

6 = (-3/4)(-5) + b

6 = 15/4 + b

6(4/4) - 15/4 = 15/4 + b - 15/4

24/4 - 15/4 = b

b = 9/4

• Now we have a line that parallel to 6x + 8y = -7 that passes through the point (-5,6)

y = (-3/4)x + 9/4

• As for the last one either it is a misprint, or you repeated the first one.

 

I hope this helps!

Answer 2

6x + 8y = -7

y = (-6x - 7)/8

m = -6/8 = -3/4

 

1.

 

A perpendicular line has slope 4/3 so the line we want is:

 

y - 6 = (4/3)(x - (-5))

 

y - 6 = (4/3)(x + 5) in point slope form

 

y = (4/3) x + 20/3 + 18/3

 

y = (4/3) x + 38/3 in slope intercept form

 

4x - 3y = -38 in standard form

 

x/(-19/2) + y/(38/3) = 1 in intercept form

 

2.

A parallel line has slope -3/4 so the line we want is:

y - 6 = (-3/4)(x - (-5))

 

y - 6 = (-3/4)(x + 5) is point slope form

 

y = (-3/4)x - 15/4 + 24/4

 

y = (-3/4)x + 9/4 is slope intercept form

 

3x + 4y = 9 is standard form

 

x/3 + y/(9/4) = 1 is intercept form

Answer 3

Hi Minalin;

6x+8y=-7,  (-5,6)

This equation is in standard format of...

Ax+By=C, neither A nor B equal zero, and A is greater than zero.

Let's convert it to slope-intercept form...

y=mx+b

m is the slope.

b is the y-intercept, the value of y when x=0.

6x+8y=-7

Let's subtract 6x from both sides...

8y=-6x-7

Let's divide both sides by 8...

y=(-6/8)x-(7/8)

y=(-3/4)x-(7/8)

slope is -3/4.

Slope of the line perpendicular to this is 4/3, the negative inverse.

y=(4/3)x+b

Let's plug-in the point provided, (-5,6)...

6=[(4/3)(-5)]+b

6=(-20/3)+b

18/3=(-20/3)+b

Let's add 20/3 to both sides...

38/3=b

y=(4/3)x+(38/3)

 

y=(-3/4)x-(7/8)

The slope of the line parallel to this is -3/4.  This line has a different y-intercept...

y=(-3/4)x+b

Let's plug-in the one point provided, (-5,6)...

6=[(-3/4)(-5)]+b

A negative number multiplied by a negative number yields a positive number...

6=(15/4)+b

24/4=(15/4)+b

Let's subtract 15/4 from both sides...

9/4=b

y=(-3/4)x+9/4

 

Answer 4

1.

 Given   L_{1 : 6X + 8Y = -7}

 

   _{find  L2 : mX + b such that    Perpendicular to L1} , passes through ( -5,6)

           

                     L_{1 : Y = - 3/4 X - 7/8}

 

            Theory :  L1   l   to L2 , if and only if m₁₌- 1

                                                                        m₂

 

                m1 = -3/4     m2 = 4/3 

 

                   L₂ :   Y = 4/3 X + b

                            6 = 4/3( -5) +b

 

                            b = 6 + 20/3 = 38/3

 

                     L2 : Y= 4/3 X + 38/3

 

      2. 

           Find L3 :  Y = m3 X  + b parallel to L1, and passes through ( -5,6 )

 

              Theory :  L1 ll to L3  if and only if m3 = m1 , m1 = -3/4

 

                Y = -3/4 X + b

                6  = -3/4( -5) +b

 

                 b = 6 - 15/4 = 9/4

 

                 Y = -3/4 X + 9/4