Answer:
Step-by-step explanation:
Temporarily substitute the = symbol in this given inequality: 3x - 4y = 8.
Now pick 2 or 3 y values and find the corresponding x value for each:
If y = 2, 3x - 4(2) = 8, so that 3x = 16 and x = 16/3. Thus, one point on the graph is (16/3, 2).
If y = 0, 3x - 4(0) = 8, and so 3x = 8, or x = 8/3. Another point on the graph is (8/3, 0).
Now plot these two points (8/3, 0) and (16/3, 2), and draw a solid line through them (because " ≥ " includes an " = " sign).
Finally, invent a 3rd point that is NOT on this solid line. Substitute the x- and y- coordinates into the original inquality 3x - 4y ≥ 8. Two possible outcomes are: a) The inequality is true. All solutions are on this side of the solid line you drew. Shade that side of the line. b) The inequality is false. Do NOT shade that side of the line.
Note: an easier way of graphing the solid line is described as follows:
Let x = 0 and find y: 3(0) - 4y = 8, so that y = -2 and a point on the line is (0, -2).
Then let y = 0 and find x: 3x = 8, or x = 8/3 and this corresponds to the point (8/3, 0) on the line.
