Graph this inequality: x – 2y ≥ 4 Plot points on the boundary line. Select the line to switch between solid and dotted. Select a region to shade it

To graph the inequality ( x – 2y geq 4 ), follow these steps:

1. Rewrite the inequality: Start by rewriting the equation ( x – 2y = 4 ) to find the boundary line. Solve for ( y ):

[

-2y = -x + 4 quad Rightarrow quad y = frac{1}{2}x – 2

]

2. Graph the boundary line:

– The line ( y = frac{1}{2}x – 2 ) has a slope of ( frac{1}{2} ) and a y-intercept at ( -2 ).

– Plot the y-intercept (0, -2) and use the slope to find another point. From (0, -2), move up 1 unit and right 2 units to plot the point (2, -1).

– Since the inequality is ( geq ), the boundary line should be solid.

3. Determine the shading region:

– To find which side of the line to shade, test a point not on the line (like (0,0)):

[

0 – 2(0) geq 4 quad Rightarrow quad 0 geq 4 quad (text{False})

]

– Since this point doesn’t