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Step-by-step explanation:
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X + 3y = 7
x = -3y + 7
2x + 4y = 8
2(-3y + 7) + 4y = 8
-6y + 14 + 4y = 8
-2y = 8 - 14
-2y = - 6
y = -6/-2
y = 3
x + 3y = 7
x + 3(3) = 7
x + 9 = 7
x = 7 - 9
x = -2
solution is (-2,3)
let's bear in mind that sin(θ) in this case is positive, that happens only in the I and II Quadrants, where the cosine/adjacent are positive and negative respectively.
![\bf sin(\theta )=\cfrac{\stackrel{opposite}{5}}{\stackrel{hypotenuse}{6}}\qquad \impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{6^2-5^2}=a\implies \pm\sqrt{36-25}\implies \pm \sqrt{11}=a \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20sin%28%5Ctheta%20%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7B5%7D%7D%7B%5Cstackrel%7Bhypotenuse%7D%7B6%7D%7D%5Cqquad%20%5Cimpliedby%20%5Ctextit%7Blet%27s%20find%20the%20%5Cunderline%7Badjacent%20side%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Ctextit%7Busing%20the%20pythagorean%20theorem%7D%20%5C%5C%5C%5C%20c%5E2%3Da%5E2%2Bb%5E2%5Cimplies%20%5Cpm%5Csqrt%7Bc%5E2-b%5E2%7D%3Da%20%5Cqquad%20%5Cbegin%7Bcases%7D%20c%3Dhypotenuse%5C%5C%20a%3Dadjacent%5C%5C%20b%3Dopposite%5C%5C%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20%5Cpm%5Csqrt%7B6%5E2-5%5E2%7D%3Da%5Cimplies%20%5Cpm%5Csqrt%7B36-25%7D%5Cimplies%20%5Cpm%20%5Csqrt%7B11%7D%3Da%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
The equation of the given Absolute Value Function is; y = |-2x + 4|
<h3>How to interpret Linear Graphs?</h3>
We can see that the given graph is a Linear graph but since it is V-shaped, we can say that it is a graph of an absolute value function.
Now, from the graph we see that;
At x = 0, y = 4
At x = 1, y = 2
At x = 2, y = 0
At x = 3, y = -2
At x = 4, y = 0
At x = 5, y = 2
We can see that the y-intercept is at y = 4.
Slope between two consecutive points is;
(2 - 4)/(1 - 0) = -2
Equation is; y = -2x + 4
Now, this is an absolute value function and as such we will write it as;
y = |-2x + 4|
Read more about Linear Graphs at; brainly.com/question/4025726
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Answer:
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