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Answer:
y < 6 + 16x
Or
y < 16x + 6
Step-by-step explanation:
The inequality 16x - y > -6 cam be rewritten in the slope-intercept form, y > mx + b as follows:
16x - y - 16x > -6 - 16x (subtraction property)
-y > -6 - 16x
Divide both sides by -1 (the inequality sign will change from > to < because we are dividing by a negative number)
-y/-1 < -6/-1 - 16/-1
y < 6 + 16x
Or
y < 16x + 6
Answer:
10
Step-by-step explanation:
We can use the point-slope equation:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
m, the slope, is 3/4:
![y = \frac{3}{4} x + b](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20%2B%20b)
To find b, we plug in the point (4,1/3):
![( \frac{1}{3} ) = \frac{3}{4} (4) + b \\ \frac{1}{3} = 3 + b \\ \frac{1}{3} = \frac{9}{3} + b](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B1%7D%7B3%7D%20%29%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%284%29%20%2B%20b%20%5C%5C%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%203%20%2B%20b%20%5C%5C%20%20%5Cfrac%7B1%7D%7B3%7D%20%3D%20%20%5Cfrac%7B9%7D%7B3%7D%20%20%2B%20b)
![- \frac{8}{3} = b](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20%20%3D%20b)
Therefore, the point-slope equation is
![y = \frac{3}{4} x - \frac{8}{3}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20)
Now we have to see which answer matches.
![y - \frac{3}{4} = \frac{1}{3} (x - 4) \\ y - \frac{3}{4} = \frac{1}{3} x - \frac{4}{3} \\ y - \frac{9}{12} = \frac{1}{3} x - \frac{16}{12}](https://tex.z-dn.net/?f=y%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%28x%20-%204%29%20%5C%5C%20y%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%5C%5C%20y%20-%20%20%5Cfrac%7B9%7D%7B12%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B16%7D%7B12%7D)
![y = \frac{1}{3} x - \frac{7}{12}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B7%7D%7B12%7D%20)
Since this is not the same, we try the next one.
![y - \frac{1}{3} = \frac{3}{4} (x - 4) \\ y - \frac{1}{3} = \frac{3}{4} x - 3 \\ y - \frac{1}{3} = \frac{3}{4} x - \frac{9}{3}](https://tex.z-dn.net/?f=y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28x%20-%204%29%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%203%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B9%7D%7B3%7D)
![y = \frac{3}{4} x - \frac{8}{3}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20)
This is the same, so this is the answer. We should still double-check the other answers.
![y - \frac{1}{3} = 4(x - \frac{3}{4} ) \\ y - \frac{1}{3} = 4x - 3 \\ y - \frac{1}{3} = 4x - \frac{9}{3}](https://tex.z-dn.net/?f=y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%204%28x%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20%29%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%204x%20-%203%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%204x%20-%20%20%5Cfrac%7B9%7D%7B3%7D)
![y = 4x - \frac{8}{3}](https://tex.z-dn.net/?f=y%20%3D%204x%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20)
This one is not equivalent.
![y - 4 = \frac{3}{4} (x - \frac{1}{3} ) \\ y - 4 = \frac{3}{4} x - \frac{1}{4} \\ y - \frac{16}{4} = \frac{3}{4} x - \frac{1}{4}](https://tex.z-dn.net/?f=y%20-%204%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28x%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%29%20%5C%5C%20y%20-%204%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%5C%5C%20y%20-%20%20%5Cfrac%7B16%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B1%7D%7B4%7D%20)
![y = \frac{3}{4} x + \frac{15}{4}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20%2B%20%20%5Cfrac%7B15%7D%7B4%7D%20)
This one also does not work.
The answer is the second one:
54.5981500331 is the answer