Since all the options are in the slope intercept form, we find the equation using the formula,
![y = mx + c](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20c)
We can find m, the slope using the formula,
![m = \frac{ change \: in \: y }{change \: in \: x}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B%20change%20%5C%3A%20in%20%5C%3A%20y%20%7D%7Bchange%20%5C%3A%20in%20%5C%3A%20x%7D%20)
![m = \frac{ - 5 - - 3}{4 - - 2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B%20-%205%20-%20-%203%7D%7B4%20-%20-%202%7D%20)
![m = \frac{ - 2}{6} = - \frac{1}{3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B%20-%202%7D%7B6%7D%20%3D%20-%20%5Cfrac%7B1%7D%7B3%7D%20)
On substitution,
![y = - \frac{ 1}{3} x + c](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%7B%201%7D%7B3%7D%20x%20%2B%20c)
We use any of the points, say (-2,-3) to determine the value of c.
![- 3 = - \frac{1}{3} ( - 2) + c](https://tex.z-dn.net/?f=%20-%203%20%3D%20-%20%5Cfrac%7B1%7D%7B3%7D%20%28%20-%202%29%20%2B%20c)
![c = - \frac{11}{3}](https://tex.z-dn.net/?f=c%20%3D%20-%20%5Cfrac%7B11%7D%7B3%7D%20)
The equation is therefore,
![y = - \frac{1}{3} x - \frac{11}{3}](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%5Cfrac%7B11%7D%7B3%7D%20)
The correct answer is D.
Answer:
<h2>12</h2>
Step-by-step explanation:
![nxy\div m\\\\n =3/4\\x =8\\y =6\\m=3\\\\\frac{3}{4} \times 8 \times 6 \div 3\\\\\mathrm{Divide\:the\:numbers:}\:6\div \:3=2\\=\frac{3}{4}\times \:8\times \:2\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:8=\frac{8}{1}\\=2\times \frac{3}{4}\times \frac{8}{1}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:2=\frac{2}{1}\\=\frac{3}{4}\times \frac{8}{1}\times \frac{2}{1}\\\\Multiply\:fractions\\=\frac{3\times \:8\times \:2}{4\times \:1\times \:1}\\\\=\frac{48}{4}\\\\Simplify\\=12](https://tex.z-dn.net/?f=nxy%5Cdiv%20m%5C%5C%5C%5Cn%20%3D3%2F4%5C%5Cx%20%3D8%5C%5Cy%20%3D6%5C%5Cm%3D3%5C%5C%5C%5C%5Cfrac%7B3%7D%7B4%7D%20%5Ctimes%208%20%5Ctimes%206%20%5Cdiv%203%5C%5C%5C%5C%5Cmathrm%7BDivide%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A6%5Cdiv%20%5C%3A3%3D2%5C%5C%3D%5Cfrac%7B3%7D%7B4%7D%5Ctimes%20%5C%3A8%5Ctimes%20%5C%3A2%5C%5C%5C%5C%5Cmathrm%7BConvert%5C%3Aelement%5C%3Ato%5C%3Afraction%7D%3A%5Cquad%20%5C%3A8%3D%5Cfrac%7B8%7D%7B1%7D%5C%5C%3D2%5Ctimes%20%5Cfrac%7B3%7D%7B4%7D%5Ctimes%20%5Cfrac%7B8%7D%7B1%7D%5C%5C%5C%5C%5Cmathrm%7BConvert%5C%3Aelement%5C%3Ato%5C%3Afraction%7D%3A%5Cquad%20%5C%3A2%3D%5Cfrac%7B2%7D%7B1%7D%5C%5C%3D%5Cfrac%7B3%7D%7B4%7D%5Ctimes%20%5Cfrac%7B8%7D%7B1%7D%5Ctimes%20%5Cfrac%7B2%7D%7B1%7D%5C%5C%5C%5CMultiply%5C%3Afractions%5C%5C%3D%5Cfrac%7B3%5Ctimes%20%5C%3A8%5Ctimes%20%5C%3A2%7D%7B4%5Ctimes%20%5C%3A1%5Ctimes%20%5C%3A1%7D%5C%5C%5C%5C%3D%5Cfrac%7B48%7D%7B4%7D%5C%5C%5C%5CSimplify%5C%5C%3D12)
Answer:
The third number is 47.
Step-by-step explanation:
The sum of three numbers is 3068 - this can be expressed mathematically as:
![\displaystyle{x + y + z = 3068}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7Bx%20%2B%20y%20%2B%20z%20%3D%203068%7D)
Given that two of the numbers are 1266 and 1755 (in order) then substitute x = 1266 and y = 1755:
![\displaystyle{1266 + 1755 + z = 3068}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B1266%20%2B%201755%20%2B%20z%20%3D%203068%7D)
Find the third number - solve for z-variable:
![\displaystyle{3021 + z = 3068}\\\\\displaystyle{z = 3068-3021}\\\\\displaystyle{z = 47}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B3021%20%2B%20z%20%3D%203068%7D%5C%5C%5C%5C%5Cdisplaystyle%7Bz%20%3D%203068-3021%7D%5C%5C%5C%5C%5Cdisplaystyle%7Bz%20%3D%2047%7D)
Therefore, the third number is 47.