what system of linear inequalities is shown in the graph? enter your answers in the boxes.
what system of linear inequalities is shown in the graph? enter your answers in the boxes.
Answer
Explanation:
Step1: Find the equation of the solid - line
The solid - line passes through points ((- 5,5)) and ((5,0)). First, find the slope (m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 5}{5+5}=-\frac{1}{2}). Using the point - slope form (y - y_1=m(x - x_1)) with the point ((5,0)), we get (y-0 =-\frac{1}{2}(x - 5)), or (y=-\frac{1}{2}x+\frac{5}{2}). Since the region is above this line and the line is solid, the inequality is (y\geq-\frac{1}{2}x+\frac{5}{2}).
Step2: Find the equation of the dashed - line
The dashed - line passes through points ((0,-3)) and ((2,1)). The slope (m=\frac{1+3}{2 - 0}=2). Using the point - slope form (y - y_1=m(x - x_1)) with the point ((0,-3)), we get (y+3 = 2(x - 0)), or (y = 2x-3). Since the region is above this line and the line is dashed, the inequality is (y>2x - 3).
Answer:
(y\geq-\frac{1}{2}x+\frac{5}{2}), (y>2x - 3)