I know that on this forum you can't graph but can someone help me with where to plot my lines... Here is the question and my solution...(need to shade solution)will draw two lines(solid) and shade below but need to verify line equation points
A small company produces both bouquets and wreaths of dried flowers. The bouquets take 1 hour of labor to produce and the wreaths take 2 hours. The labor available is limited to 80 hours per week, and the total production capacity is 60 items per week. Write a system of inequalities representing this situation, where x is the number of bouquets and y is the number of wreaths. Then graph the system of inequalities.
answer
x=bouquets
y=wreaths
x+y<=60 so y<=-x+60
x+2y<=80 so y<=-x/2+40
just look at the formula for the eq. for the first one, the y-int. is 60 with a slope of -1, so the x-int. is also 60. for the 2nd eq., y-int=40 & slope is -1/2 with x-int. of 80
To graph the system of inequalities, you can use the slope-intercept form of the equations. Let's start with the first equation:
y <= -x + 60
The y-intercept is 60, and the slope is -1. Plot the y-intercept at (0, 60), and then use the slope to find another point. Since the slope is -1, you can go down 1 unit and to the right 1 unit to get another point. Draw a solid line through these two points.
Next, let's graph the second equation:
y <= -x/2 + 40
The y-intercept is 40, and the slope is -1/2. Plot the y-intercept at (0, 40), and then use the slope to find another point. Since the slope is -1/2, you can go down 1 unit and to the right 2 units to get another point. Draw a solid line through these two points.
Now, to shade the area that satisfies both inequalities, you need to determine which region satisfies both conditions. Since the problem states that the number of bouquets and wreaths needs to be less than or equal to 60, and the number of labor hours needs to be less than or equal to 80, the shaded region will be below both lines.
To shade the region, you can either shade below both lines on your graph or write the shaded region as an inequality:
y <= -x + 60
y <= -x/2 + 40
Intuitively, it means that any point that satisfies both inequalities will be below both lines on the graph.
I hope that helps! Let me know if you have any further questions.