First let's assume that the table contains points on a straight line. Then all we have to do is to determine the slope of that line.
Suppose we go from (0,3) to (7,-28.5).
-28.5-3 -31.5
Then the slope, m, is m = ------------- = ---------- = - 9/2, or - 4.5.
7-0 7
Let's check this result!
Suppose that y = mx + b governs the relationship between x and y.
Then y = -4.5x + b
suppose we find b by substituting the coordinates from the point (0,3):
3 = -4.5(0) + b
Then b = 3, and y = -4.5x + 3. Does the point (-2,12) satisfy this equation?
Does 12 = -4.5(-2) + 3? Does 12 = 9 + 3? YES.
So y = -4.5x + 3 is the equation from which these points came, and the rate of change of y with respect to x is the slope m = -4.5, or m = -9/2.
![\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse} \quad % tangent tan(\theta)=\cfrac{opposite}{adjacent}\\\\ -------------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20sin%28%5Ctheta%29%3D%5Ccfrac%7Bopposite%7D%7Bhypotenuse%7D%0A%5Cqquad%0Acos%28%5Ctheta%29%3D%5Ccfrac%7Badjacent%7D%7Bhypotenuse%7D%0A%5Cquad%20%0A%25%20tangent%0Atan%28%5Ctheta%29%3D%5Ccfrac%7Bopposite%7D%7Badjacent%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C)
![\bf sin(\theta )=\cfrac{2}{7}\cfrac{\leftarrow opposite}{\leftarrow hypotenuse}\qquad \textit{let's find the 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{7^2-2^2}=a\implies \pm\sqrt{45}=a\implies \pm 3\sqrt{5}=a](https://tex.z-dn.net/?f=%5Cbf%20sin%28%5Ctheta%20%29%3D%5Ccfrac%7B2%7D%7B7%7D%5Ccfrac%7B%5Cleftarrow%20opposite%7D%7B%5Cleftarrow%20hypotenuse%7D%5Cqquad%20%5Ctextit%7Blet%27s%20find%20the%20adjacent%20side%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Busing%20the%20pythagorean%20theorem%7D%5C%5C%5C%5C%0Ac%5E2%3Da%5E2%2Bb%5E2%5Cimplies%20%5Cpm%5Csqrt%7Bc%5E2-b%5E2%7D%3Da%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Ac%3Dhypotenuse%5C%5C%0Aa%3Dadjacent%5C%5C%0Ab%3Dopposite%5C%5C%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cpm%5Csqrt%7B7%5E2-2%5E2%7D%3Da%5Cimplies%20%5Cpm%5Csqrt%7B45%7D%3Da%5Cimplies%20%5Cpm%203%5Csqrt%7B5%7D%3Da)
but.... which is it? the + or the -? well, we know that tan(θ) > 0, is another way to say that the tangent of the angle is positive, now, for the tangent to be positive, since it's opposite/adjacent both opposite and adjacent have to be the same exact sign, now, we know the opposite is +2, so that means the adjacent has to be the same sign, thus is the positive version 3√(5)
thus
U plot ur answers on the graph and u will fid it
Answer:
(-7,-1)
Step-by-step explanation: