Write an equation containing the points (7,6) and perpendicular to 3x-8y=69

Question

really need to answer this by today !!!!!!

Answer 1

First, the slopes of 2 perpendicular lines are negative reciprocals of each other. So, we must find what the slope of the original equation is. Remember:

                            y = mx + b  where "m" is the slope and "b" is the y-intercept

                            3x - 8y = 69  original equation

                            3x - 69 = 8y  rearrange to get "y" by itself

                           (3x - 69)/8 = y  divide both sides by 8

                           y = (3/8)x - (69/8)  in the form of y = mx + b

We see that the slope is +3/8, so the negative reciprocal will be -8/3 which is "m" of the perpendicular line. Using the point (7,6) we can find the y-intercept, b, of the new line:

                          y = mx + b  equation of a line

                          6 = (-8/3)(7) + b  putting in what we know

                          6 = (-56/3) + b

                          6 + (56/3) = b  add (56/3) to both sides

                         (18/3) + (56/3) = b  getting a common denominator

                         (74/3) = b  solve for b

We now know that m = (-8/3) and b = (74/3) for the perpendicular line, so let's put all this info into the general equation of a line:

                         y = mx + b  equation of a line

                         y = (-8/3)x + (74/3)  substituting what we know

                        3y = -8x + 74  multiply everything by 3 to get rid of the fractions

                        8x + 3y = 74  put into standard form

Therefore, the answer is 8x + 3y = 74.

                          

 

Answer 2

Perpendicular lines have slopes that are negative reciprocals of each other

m(m_⊥) = -1

 

3x-8y=69

slope of ax + by = c is given by m = -a/b

Slope of this line is -3/(-8) = 3/8

 

Perpendicular slope is -8/3

 

You are looking for the equation of a line with slope -8/3 through (7, 6):

For slope intercept form we have y = mx + b

y = (-8/3)x + b  through (7, 6).

 

Using (7, 6) for (x, y) to find b:

6 = (-8/3)(7) + b

6 = -56/3 + b

b = 6 + 56/3 = 18/3 + 56/3 = 74/3

 

Your equation is:  y = (-8/3)x + 74/3

 

Putting this back into standard format of ax + by = c

 

3y = -8x + 74

8x + 3y = 74