Dotted line joining negative 1, negative 2 and 3,0 and the region below the line is shaded. Which of the following inequalities is best represented by this graph?
A) x − 2y > 3
B) x − 2y < 3
C) 2x − y > 3
D) 2x − y < 3
The two points are (-1,-2) and (3,0). Let's find the slope of the line through these points
m = (y2 - y1)/(x2 - x1) m = (0 - (-2))/(3 - (-1)) m = (0 + 2)/(3 + 1) m = 2/4 m = 1/2
Plug this m value and one of the points into the equation y = mx+b. Solve for b. I'll use (x,y) = (-1,-2) as the point of choice
y = mx+b -2 = (1/2)*(-1)+b -2 = -1/2+b -2+1/2 = b b = -4/2+1/2 b = -3/2
So the boundary line equation is y = (1/2)x-3/2 The shading is below the boundary line equation. The boundary is dashed. So we have this inequality y < (1/2)x - 3/2 Now we must get the inequality either in the form Ax+By < C or Ax+By > C
Let's do that to get... y < (1/2)x - 3/2 2y < x - 3 -x+2y < -3 -1*(-x+2y) > -1*(-3) x-2y > 3
