Answer: A. The wrong region is shaded
Step-by-step explanation:
Let's solve for y in the first equation.
3x−2y<−5
Step 1: Add -3x to both sides.
3x−2y+−3x<−5+−3x
−2y<−3x−5
Step 2: Divide both sides by -2.
[tex]\frac{-2y}{-2}[/tex]< [tex]\frac{-3x-5}{-2}[/tex]
y > [tex]\frac{3}{2}x+\frac{5}{2}[/tex]
graph the equation using the slope [tex]\frac{3}{2}[/tex] and the y-intercept [tex]\frac{5}{2}[/tex]
The line is dotted because it is > (not ≥)
shade in the left side by plugging in (0,0) into x and y and finding
0 is not > than [tex]\frac{5}{2}[/tex]. This means you shade in the side not include the origin.
Do this same thing for the next equation.
Let's solve for y in the second equation.
x+4y>8
Step 1: Add -x to both sides.
x+4y+−x>8+−x
4y>−x+8
Step 2: Divide both sides by 4.
[tex]\frac{4y}{4}[/tex] > [tex]\frac{-x+8}{4}[/tex]
y > [tex]\frac{-1}{4}x+2[/tex]
graph the equation using the slope [tex]-\frac{1}{4}[/tex] and the y-intercept 2
(Dotted line), (plug in 0,0 and find 0 is not > than 2. So shade the region not including the origin (0,0).
Hope this helps.
