Question:
Solution:
Step 1: Find the equation of a line:
Notice that the line passes through the point (x2,y2)= (4,-2) and (x1,y1)=(0,3). Then, the slope of this line would be:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}=\text{ }\frac{-2-3}{4-0}\text{ = }\frac{-5}{4}\text{ =-}\frac{5}{4}[/tex]
now, notice that the y-intercept of this line is b=3. Then, the equation for this line is:
[tex]y\text{ = -}\frac{5}{4}x+3[/tex]
Step 2:
note that the shaded region is all points on the line and those above it. So, the shaded region can be represented by the following inequality:
[tex]y\text{ }\ge\text{ -}\frac{5}{4}x+3[/tex]
and it is shown graphically like this:
So that, we can conclude that the correct answer is:
[tex]y\text{ }\ge\text{ -}\frac{5}{4}x+3[/tex]
