Answer:
A) x = 2; y = 2; (m, n) = (1/2, 0); (p, q) = (-3/2, 12)
B) K; A and E
C) 11
Explanation:
With the exception of the vertical line, the equations of the lines can be written in terms of their slope and y-intercept. The slope is the ratio of "rise" to "run". The "rise" is the vertical change between points, and the "run" is the horizontal change between the same points. Changes to the right or up are taken as positive. The change amounts can be read from the graph by counting grid squares, or by subtracting coordinate values.
The regions described by an inequality will be to the right of a boundary line for x > (boundary), and above the boundary line for y > (boundary). When these inequalities are reversed, the region will be left or below the boundary, respectively.
__
A)
The slope-intercept equation for a line is ...
y = mx +b . . . . where m is the slope, and b is the y-intercept
(i) x = 2 . . . . . . points on the vertical line have an x-value of 2
(ii) y = 2 . . . . . 0 slope, y-intercept of 2
(iii) m = 1/2, n = 0 . . . . rise = 1 for run = 2; y-intercept = 0
(iv) p = -3/2, q = 12 . . . . rise = -3 for run = 2; y-intercept = 12
__
B)
(i) Region K is to the right of the vertical line, and above the two slanted lines
(ii) Regions A and E are below y=2 and the two slanted lines
__
C)
The maximum value of x+y will be found at the point on the line x+y=c, where c is the largest possible value. That is, it will lie on the line ...
y = -x +c . . . . a line with a slope of -1
such that the line is as far as possible from the origin.
For region G, the point that maximizes "c" in the above equation is point (2, 9), so ...
c = x +y = 2 +9 = 11
The maximum value of (x+y) in region G is 11.