On a house plan, the floor area of a room measures 4 1/4. by 3 1/2 in. If 1 /4 in. is equal to 1 ft on the drawing, what are the actual dimensions of the room?

7 ft by 17 ft

Step-by-step explanation:

Our goal is to express the actual dimensions of the room in square feet.

The first dimension on the drawing, 4 1/4 in, corresponds to 17 ft of actual length of the room, as seen below:

We write and solve an equation of ratios:  

(4 1/4 in)      1/4 in

=  which comes out to (4 1/4 in)(1 ft) = (1/4 in)(x), or

      x            1 ft

                                 17 in-ft = x in, or x = 17 ft is the actual room length

and the actual room width is

(3 1/2 in)       1/4 in

= , which yields room width y = 7 ft

       x             1 ft

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0