The inequality is represented by y < 5/3(x+1)
Use the information about the straight line and find the equation of the line.
Given coordinates (-3,-4) and (0,1), we can find the slope
Slope,
Change in y = y2 – y1 = 1-(-4) = 5
Change in x = x2 – x1 = 0-(-3) = 3
Therefore, Slope (m) = Change in y / Change in x = 5/3
Equation of line using m = 5/3 and points (0,1) and (x, y) in form of y = mx + c
Y – 1/ X – 0 =5/3
3(Y-1) = 5(X)
3Y -3 = 5X
3Y = 5X + 3
Y = 5X + 3/3
Y = 5/3(X + 1)
To find the inequality take a point in the shaded region and check it in the above equation.
Given Options
a. y < Five-thirds x – 2
b. y < Negative five-thirds x + 1
c. y > Five-thirds x + 2
d. y > Negative five-thirds x + 2
Let’s take points (-3,-4) for verification
Option a: y < 5/3 (x-2)
-4 < 5/3(-3-2)
--4 < -3.33
-4 is less than -3.33
Thus option a is in the shaded region
Option b: y < -5/3 (x+1)
-4 < -5/3(-3+1)
--4 < 3.33
-4 is less than 3.33
Thus option a is in the shaded region
Option c: y > 5/3 (x+2)
-4 > 5/3(-3+2)
--4 > -1.67
-4 is NOT GREATER than -1.67
Thus option c is NOT in the shaded region
Option d: y > -5/3 (x+2)
-4 > - 5/3(-3+2)
--4 > 1.67
-4 is NOT GREATER than 1.67
Thus option d is NOT in the shaded region
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