Consider the line y = -7x+6.
find the equation of the line that is parallel to this line and passes through the point (
5
5
)
find the equation of the line that is perpendicular to this line and passes through the point (5,-5).

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have the following equation:

With slope

By definition, if two lines are parallel then their slopes are equal. Thus, a parallel line will be of the form:

We replace the point (5,5) through which the line passes and find "b":

Finally, the equation is:

On the other hand, if two lines are perpendicular then the product of their slopes is -1. Thus, the slope of a perpendicular line will be:

Thus, the equation is of the form:

We substitute the point (5, -5) through which the line passes and find "b":

Finally, the equation is:

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you