use the equation k = x + y to find the constant of proportionality for the set of values below. then…

use the equation k = x + y to find the constant of proportionality for the set of values below. then, complete the table with three more values. graph the points on the coordinate plane, draw a line through the points, and answer the question.\n\nhow does the graph show that the rate of change is constant?\n\nmatch each word with another word that has a similar denotation but a different connotation. write the letter of the matching word on the line.\n1. skinny\n2. fragrance\n3. assertive\n4. smile\n5. thrifty\n6. home\n7. stare\n8. shrewd\na. aggressive\nb. residence\nc. smirk\nd. glower\ne. clever\nf. odor\ng. stingy\nh. slender

Answer

Explanation:

Step1: Find the constant of proportionality

When (x = 1) and (y=3), using (k=x + y), we have (k=1 + 3=4).

Step2: Complete the table

Since (k=x + y = 4), when (x = 2), (y=6) (this seems to be an error in the problem - it should follow (y=k - x)). For new values: If (x=3), then (y=k - x=4 - 3 = 1); if (x = 4), then (y=4 - 4=0); if (x=0), then (y=4-0 = 4).

Step3: Analyze the rate - of - change for the graph

The rate of change of a linear function (y=-x + k) (rewritten from (k=x + y)) is (- 1). On a graph, a constant rate of change is shown by a straight - line. The slope between any two points ((x_1,y_1)) and ((x_2,y_2)) is (m=\frac{y_2 - y_1}{x_2 - x_1}), and for (y=-x + 4), the slope is (-1) everywhere, so the graph is a straight line.

Step4: Match words

skinny - h. slender (both mean thin, but “skinny” can have a more negative connotation)
fragrance - f. odor (both refer to a smell, but “fragrance” is more positive)
assertive - a. aggressive (both imply confidence, but “aggressive” is more negative)
smile - c. smirk (both involve facial expressions, but “smirk” has a negative connotation)
thrifty - g. stingy (both relate to saving money, but “stingy” is negative)
home - b. residence (both refer to a place of living, but “home” has more emotional connotation)
stare - d. glower (both involve looking, but “glower” has a more negative, angry connotation)
shrewd - e. clever (both mean intelligent, but “shrewd” can have a more calculating connotation)

Answer:

(k = 4) The completed table:

(x)	(y)
(1)	(3)
(2)	(2)
(3)	(1)
(4)	(0)
(0)	(4)
The graph shows a constant rate of change because it is a straight - line.