Which is the graph of 4x-8y<=9
1 answer:
Given inequality is
Now we need to find the graph of .
Which can be done into two parts:
First graph the line then shade the graph for inequality sign
Graph the line
we can plug any number for x say x=0 to find the y-value
4x-8y=9
4*0-8y=9
0-8y=9
-8y=9
y=-1.125
Hence first point is (0,-1.125)
Similarly we can plug y=0 then solve for x
4x-8y=9
4x-8*0=9
4x-0=9
4x=9
x=2.25
hence 2nd point is at (2.25,0)
Now graph both points and join them by a straight line.
Since used inequality is so we use solid line not the dotted line.
Shading the graph:
we can pick any test point which is not on the line 4x-8y=9 say (0,0) then plug into original problem to see if that point satisfies the original problem or not.
Which is TRUE.
TRUE means shade in direction of test point otherwise we graph in opposite direction of test point.
Now final graph will look like the graph attached below:
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Answer: The flowchart is shown below.
Explanation:
Each box is a different statement. The reason for the statement is provided below the box. The arrows on the flowchart direct the flow of how the proof is laid out. Typically the flow is left to right, top to bottom, or a mix of both. This is to match the reading order of many western countries. Though I would imagine the flow is reversed for countries that read from right to left.
The structure of any type of proof is to start with what you are given. Then use the previously established, or previously proven, theorems to make your way to what you want to prove.
In this case, we start off with MN and KL being parallel line segments. This is shown by the arrows on MN and KL. Because the segments are parallel, we then can determine these two facts:
- angle MNJ = angle KLJ
- angle NMJ = angle LKJ
Both of those will have the reasoning of "corresponding angles theorem"
We have two pairs of angles which are congruent. This then directly leads to the triangles being similar. Refer to the AA (angle angle) similarity theorem for more information.
Feel free to use symbols in place of some words. For example, instead of saying something like "Triangle NMJ is similar to Triangle LKJ", you could write
If you're curious what app I used to make the flowchart, the app is called "LucidChart". They have 3 options: 1 free and the other 2 are paid versions. I went with the free version and it worked just fine. But it's up to you which you prefer most.
