which system of linear inequalities is represented by the graph?\n○ ( y geq x - 2 ) and ( x - 2y < 4 )\n○ (…

which system of linear inequalities is represented by the graph?\n○ ( y geq x - 2 ) and ( x - 2y < 4 )\n○ ( y geq x + 2 ) and ( x + 2y < 4 )\n○ ( y geq x - 2 ) and ( x + 2y < 4 )\n○ ( y > x - 2 ) and ( x + 2y < - 4 )

which system of linear inequalities is represented by the graph?\n○ ( y geq x - 2 ) and ( x - 2y < 4 )\n○ ( y geq x + 2 ) and ( x + 2y < 4 )\n○ ( y geq x - 2 ) and ( x + 2y < 4 )\n○ ( y > x - 2 ) and ( x + 2y < - 4 )

Answer

Explanation:

Step1: Find the equation of the first line

The first line has a (y)-intercept of (- 2) and a slope (m = 1) (using the formula (m=\frac{y_2 - y_1}{x_2 - x_1}), for points ((0,-2)) and ((2,0))). The equation of the line is (y=x - 2). The shaded region is above this line and the line is solid, so the inequality is (y\geq x - 2).

Step2: Find the equation of the second line

Rewrite (x + 2y=4) in slope - intercept form (y=-\frac{1}{2}x + 2). The line (x + 2y = 4) has a (y)-intercept of (2) and a slope of (-\frac{1}{2}). The shaded region is below this line and the line is dashed, so the inequality is (x + 2y<4).

Answer:

(y\geq x - 2) and (x + 2y<4) (the third option)