SOLUTION: find the graphical solution of the inequality 8x+9y<0

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Question 105810: find the graphical solution of the inequality 8x+9y<0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

8x%2B9y%3C0
first, find a graph of 8x%2B9y=0 to see the point where this finction is equal to 0
as you will see on the graph, the line goes through 0%2C0, and it is decreasing
for all x where x%3E0 and x=+infinity, y will be < then 0,
so, shade the area between x-axis and line to the right from 0 (excluding 0)

Solved by pluggable solver: Graphing Linear Equations


8%2Ax%2B9%2Ay=0Start with the given equation



9%2Ay=0-8%2Ax Subtract 8%2Ax from both sides

y=%281%2F9%29%280-8%2Ax%29 Multiply both sides by 1%2F9

y=%281%2F9%29%280%29-%281%2F9%29%288%29x%29 Distribute 1%2F9

y=0%2F9-%288%2F9%29x Multiply

y=%28-8%2F9%29%2Ax%2B0%2F9 Rearrange the terms

y=%28-8%2F9%29%2Ax%2B0 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-8%2F9 (the slope) and b=0 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-9

y=%28-8%2F9%29%2A%28-9%29%2B0

y=72%2F9%2B0 Multiply

y=72%2F9 Add

y=8 Reduce

So here's one point (-9,8)





Now lets find another point

Plug in x=0

y=%28-8%2F9%29%2A%280%29%2B0

y=0%2F9%2B0 Multiply

y=0%2F9 Add

y=0 Reduce

So here's another point (0,0). Add this to our graph





Now draw a line through these points

So this is the graph of y=%28-8%2F9%29%2Ax%2B0 through the points (-9,8) and (0,0)


So from the graph we can see that the slope is -8%2F9 (which tells us that in order to go from point to point we have to start at one point and go down -8 units and to the right 9 units to get to the next point), the y-intercept is (0,0)and the x-intercept is (0,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=0 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,0).


So we have one point (0,0)






Now since the slope is -8%2F9, this means that in order to go from point to point we can use the slope to do so. So starting at (0,0), we can go down 8 units


and to the right 9 units to get to our next point



Now draw a line through those points to graph y=%28-8%2F9%29%2Ax%2B0


So this is the graph of y=%28-8%2F9%29%2Ax%2B0 through the points (0,0) and (9,-8)