Answer:
Choice B
y < 4
y ≥ 4x - 4
Explanation:
The shaded blue area is the region which satisfies both inequalities.
It is formed by two lines
A horizontal dotted line which passes through y = 4
The equation of such a line is y = 4
The dotted line represents a less than inequality so the region should be satisfied by either y < 4 or y > 4
Looking at the answer choices we see that no answer choice has y > 4. Also choice D has y ≤ 4 rather than y < 4 so we can ignore D
For the second line we note that it is a solid line representing either a ≤ or a ≥ inequality for the shaded region
Let's find the equation for this line in slope-intercept form i.e. y = mx + b where m = slope and b = -intercept
- The line passes through (0, - 4) and (1, 0)
- The slope of the line is
- The y-intercept is the y-value where the line crosses the y-axis at x = 0 and we see that it is -4
- So the equation of the line is y = 4x - 4
We can eliminate C
We have to figure out which inequality is the shaded region
To do this:
Take any point in the shaded region
Take (0,0)
For option A
Find if the y-value=0 for x = 0 is satisfied in inequality y ≤ 4x - 4
This would be 0 ≤ 4(0) - 4
0 ≤ 0 - 4
0 ≤ -4 which is false since 0 is always greater than negative values
So the correct choice is B
y < 4
y ≥ 4x - 4
You can double-check by using the same point (0,0) and plugging it into the ≥ inequality to see if it satisfies, which it does