Answer:
(a) See attachment 1
(b) See attachment 2
Step-by-step explanation:
Part (a)
To draw the line y = 1 on the given coordinate plane, draw a horizontal line parallel to the x-axis that passes through y = 1.
To draw the line x = 2 on the given coordinate plane, draw a vertical line parallel to the y-axis that passes through x = 2.
To draw the line x + y = 7, first rearrange it into slope-intercept form by isolating y:
[tex]x + y = 7\\\\x + y-x = 7-x\\\\y = -x + 7[/tex]
Therefore, the line crosses the y-axis at (0, 7).
Its x-intercept is the value of x when y = 0:
[tex]0=-x+7\\\\x=7[/tex]
Therefore, the line crosses the x-axis at (7, 0).
Draw line x + y = 7 by plotting points (0, 7) and (7, 0) on the given coordinate plane, and connecting them with a straight line.
[tex]\dotfill[/tex]
Part (b)
The inequality sign "≥" means "greater than or equal to."
To show the inequality y ≥ 1 on the given coordinate plane, shade above the line y = 1.
To show the inequality x ≥ 2 on the given coordinate plane, shade to the right of the line x = 2.
The inequality sign "≤" means "less than or equal to."
To show the inequality x + y ≤ 7 on the given coordinate plane, shade below the line y = -x + 7.
The region that satisfies all three inequalities is the overlapping shaded region. Label this region region R. (See attachment).
