Rectangle TUVW is on a coordinate plane at T (a, b), U (a + 2, b + 2), V (a + 5, b − 1), and W (a + 3, b − 3). What is the slope of the line that is parallel to the line that contains side WV? A.) −2 B.) 2 C.) −1 D.) 1

Explanation:

W = (a+3, b-3)

V = (a+5, b-1)

Let (x1,y1) = (a+3, b-3) and (x2,y2) = (a+5, b-1)

Compute the slope using the slope formula

m = slope

m = (y2 - y1)/(x2 - x1)

m = ( (b-1) - (b-3) )/( (a+5) - (a+3) )

m = (b-1 - b+3)/(a+5 -a-3)

m = 2/2

m = 1

Conveniently all the variable terms (of 'a's and 'b's) cancel out leaving us with a single number. It doesn't matter what the value of 'a' or 'b' is, as the slope of WV is always 1.

The slope of any parallel line to WV will also be 1 as well. Parallel lines have equal slopes, but different y intercepts.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

answer: b.

step-by-step explanation:

the y coordinate for point b is 0, and answer b is the only one with that y coordinate.