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Question 934305: Jason wants to buy rose plants and sunflower plants for his garden. Rose plants cost $10 each, and sunflower plants cost $15 each and his spending limit is $300. The inequality 10x+15y is equal to or greater than 300 models the total amount of money Jason can spend on plants, where x represents the number of rose plants and y represents the number of sunflowers plants. Graph the inequality.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the equation is 10x + 15y <= 300
this is because the total that he spends has to be less than or equal to 300.
to graph this inequality, you would graph the equality and then look for the area on the graph that represents the inequality.
the equation you graph would be:
10x + 15y = 300
to graph it, solve for y to get:
y = (300 - 10x) / 15
you can simplify this, and you can put it in slope intercept form, but it's not necessary.
it will graph the same either way.
i'll convert it for you so you can see how it works.
start with y = (300 - 10x) / 15
distribute the division to get:
y = 300 / 15 - 10x / 15
simplify to get:
y = 20 - 2/3 * x
re-order the terms to get:
y = - 2/3 * x + 20
- 2/3 is the slope
20 is the y intercept.
to manually graph it, you pick 2 values of x and solve for y and then draw a straight line between them.
to use graphing software, you merely enter the equation into the graphing software and it will show you the graph, assuming you have set the scale of the x and y axis correctly.
the graph of that equation looks like this:
once you graph it, you look for the area that satisfies the inequality.
the area on that graph that satisfies the inequality is all points on the graph that are below the line y = -2/3 * x + 20,
you would shade that area to show you that it is the area on the grpah that satisfies the inequality.
if it's hard to see, you simply find one value of x that is on the graph and then look for a value of y that is below that.
for example, when x = 15, y will be equal to -2/3 * 20 + 20 which will be equal to -10 + 20 which will be equal to 10.
the coordinate point on the line when x = 15 will be (15,10).
i drew a horizontal line on the graph at y = 10. look at the intersection of that horizontal line with the graph of the equation and then look vertically down from there and you will see that x = 15 at that point.
when x = 15, any value of y less than 10 will be below the line and any value of y greater than 10 will be above the line.
since you are looking for all values of y smaller than or equal to 10, than any value of y less than 10 will satisfy the inequality portion of the equation and will be below the line.
you can do the same analysis for any other point on the line.
evaluate the equality portion of the equation at any other point on the line to find the value of y that will be on the line at that value of x.
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