SOLUTION: How do I graph 2y-5x<13

Question 349098: How do I graph 2y-5x<13
Found 3 solutions by mananth, stanbon, Theo:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
2y-5x<13
2y<5x+13
y<5x/2 +13/2
assume an = sign for finding the values of x ,y
plug three or more values of x (say 1,2,3) and calculate y..
Plot the points xy and draw a line.
since y < something all values below the line will be the solution for the inequality
..

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
How do I graph 2y-5x<13
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Note: You NEVER graph an inequality directly.
You graph the boundary, which is an equality.
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1st: Solve for "y"
2y < 5x+13
y < (5/2)x + (13/2)
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2nd: Graph y = (5/2)x+(13/2)
as a dashed line. That is the boundary.
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3rd: Shade the halp-plane BELOW the boundary
because you want y to be LESS than (5/2)x+(13/2).
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That is the graph of the inequality.
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Cheers,
Stan H.
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
you need to solve for y.

then you can graph it.

2y-5x < 13

add 5x to both sides to get:

2y < 5x + 13

divide both sides by y to get:

y < (5x+13)/2

now you can graph the equation of:

y = (5x+13)/2.

any value of y below the the graph of that equation is good.

any value of y on or higher than the graph of that equation is not good.

you would shade the area of the graph below the line to indicate that is the good region.

your graph would look like this:

to prove your graph is good, take the value of x = 0 and substitute it in your equation to get:

y = (5x+13)/2 which becomes y = 13/2 which becomes y = 6.5 which is confirmed by the graph of the equation crossing the y-axis at x = 6.5.

to further prove your graph is good, take the value of y = 0 and substitute it in your equation to get:

0 = (5x+13)/2.

multiply both sides of the equation to get:

0 = 5x + 13

subtract 13 from both sides of the equation to get:

-13 = 5x

divide both sides of the equation by 5 to get:

-13/5 = x

-13/5 is equal to -2.6 which is the value of y when x = 0 and is confimred by the graph crossing the x-axis at approximately that point.

you don't graph the inequality directly.

you graph the equality and then apply logic so see where the values of y can lie.

in this case the values of y that lie below the equation are the values that are valid.

take any value of x.

find the value of y that lies on the graph of the equation of y = (5x+13)/2.

for that value of x, any value of y less than that will be below the line, and any value of y greater than that will be above the line.

the region that is valid for the equation y < (5x+13)/2 will be below the line.

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