Answer:
[tex]\large\boxed{Q1.\ \left\{\begin{array}{ccc}y\leq-2x-1\\y\leq x+5\end{array}\right}\\\boxed{Q2.\ 6\leq y-3\leq8}\\\boxed{Q3.\ y\leq x-4}[/tex]
Step-by-step explanation:
<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded above the line
>, ≥ - shaded below the line
=================================================
The slope intercept form of a line: y = mx + b
m - slope
b - y-intercept (0, b)
If m > 0, then the function is increasing
If m < 0, then the function is decreasing
==================================================
Q1.
y = -2x - 1 → m = -2 < 0 and b = -1
decreasing function, y-intercept -1 → (0, -1)
y = x + 5 → m = 1 > 0 and b = 5
increasing function, y-intercept 5 → (0, 5)
y = 2x - 1 → m = 2 > 0, and b = -1
increasing function, y-intercept -1 → (0, -1)
y = -x + 5 → m = -1 < 0 and b = 5
decreasing function, y-intercept 5 → (0, 5)
From the picture we have
(1) increasing function and y-intercept 5 → y = x + 5
shaded below the solid line → y ≤ x + 5
(2) decreasing function and y-intercept -1 → y = -2x - 1
shaded below the solid line → y ≤ -2x - 1
=======================================================
Q2.
[tex]9\leq y\leq11[/tex] subtract 3 from both sides
[tex]9-3\leq y-3\leq11-3\\\\6\leq y-3\leq8[/tex]
=======================================================
Q3.
solid line (≤ or ≥)
shaded below the line (≤ or <)
y ≤ x - 4
