Graph D represents the solution to the system of linear inequalities.
The system of inequalities is:
x - 3y ≤ 32
2x + 5y ≥ 10
We can solve this system of inequalities by graphing each inequality and then finding the region that is common to both graphs.
To graph the first inequality, x - 3y ≤ 32, we can rewrite it in y = mx + b form.
y = (1/3)x - 10
The y-intercept for the first inequality is -10. So the first line must pass through the point (0, -10).
The slope for the first inequality is 1/3. Remember that the slope tells you rise over run. So in this case for every 1 position you move up You must also move 3 positions to the right.
Graph the blue line so it passes through (0, -10) and has a slope of 1/3.
To graph the second inequality, 2x + 5y ≥ 10, we can rewrite it in y = mx + b form.
y = (-2/5)x + 2
The y-intercept for the second inequality is 2. So the second line must pass through the point (0, 2).
The slope for the second inequality is -2/5. Remember that the slope tells you rise over run. So in this case for every 2 positions you move down (because it's negative) You must also move 5 positions to the right.
Graph the green line so it passes through (0, 2) and has a slope of -2/5.
The solution to the system of inequalities is the shaded region that is common to both graphs.
The shaded region is the triangle that is bounded by the x-axis, the blue line, and the green line.
Only the graph in choice D satisfies the above conditions.