Answer:
45
Step-by-step explanation:
the slope is 8/3 so you can use y = 8/3x
make the y-value equal to 120
120 = 8/3x
cross-multiply to get:
8x = 360
x = 45
Graph 1: Domain = 2 <= x < 12
Graph 1: Range = {2,4}
Graph 2: Domain = 3 <= x <= 10
Graph 2: Range = -6 <= y <= 4
Graph 3: Domain = 4 < x < 11
Graph 4: Range = -6 <= y < 2
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![\text{\textbf{Hello!} In this question, we are trying to figure out the \underline{equation} of the line}\\\text{with the given information.}](https://tex.z-dn.net/?f=%5Ctext%7B%5Ctextbf%7BHello%21%7D%20In%20this%20question%2C%20we%20are%20trying%20to%20figure%20out%20the%20%5Cunderline%7Bequation%7D%20of%20the%20line%7D%5C%5C%5Ctext%7Bwith%20the%20given%20information.%7D)
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![\textbf{Explanation:}\\\quad{}\\\text{In the question, we were given our \emph{slope} (gradient) and a \emph{point}. This will help}\\\text{us solve our problem.}\quad{}\\\\\text{Slope: 2 }\\\\\text{Point: (1, 4)}\\\quad{}\\\text{In order to find the equation, we will be using the \underline{point-slope formula:}}\\\quad{}\\y - y1 = m(x - x1)\\\quad{}\\\text{With this equation, we would plug in our given values to its}\\\text{correct variable and solve.}](https://tex.z-dn.net/?f=%5Ctextbf%7BExplanation%3A%7D%5C%5C%5Cquad%7B%7D%5C%5C%5Ctext%7BIn%20the%20question%2C%20we%20were%20given%20our%20%5Cemph%7Bslope%7D%20%28gradient%29%20and%20a%20%5Cemph%7Bpoint%7D.%20This%20will%20help%7D%5C%5C%5Ctext%7Bus%20solve%20our%20problem.%7D%5Cquad%7B%7D%5C%5C%5C%5C%5Ctext%7BSlope%3A%202%20%7D%5C%5C%5C%5C%5Ctext%7BPoint%3A%20%281%2C%204%29%7D%5C%5C%5Cquad%7B%7D%5C%5C%5Ctext%7BIn%20order%20to%20find%20the%20equation%2C%20we%20will%20be%20using%20the%20%5Cunderline%7Bpoint-slope%20formula%3A%7D%7D%5C%5C%5Cquad%7B%7D%5C%5Cy%20-%20y1%20%3D%20m%28x%20-%20x1%29%5C%5C%5Cquad%7B%7D%5C%5C%5Ctext%7BWith%20this%20equation%2C%20we%20would%20plug%20in%20our%20given%20values%20to%20its%7D%5C%5C%5Ctext%7Bcorrect%20variable%20and%20solve.%7D)
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![\textbf{Solve:}\\\\\text{Use the point-slope formula to solve.}\\\\y - y1 = m(x - x1)\quad{}\\\\\text{Plug in 2 to m, 1 to x1, 4 to y1 and then solve.}\\\\y - 4 = 2(x - 1)\\\\\text{Use the \underline{distributive property} to distribute the 2.}\\\\y - 4 = 2x - 2\\\\\text{Add 4 to both sides to cancel the 4 on the left and move the remainder}\\\text{to the right side of the equal sign.}\\\\y = 2x + 2\\\\\text{Since we can't simplify any further, our answer is: \fbox{y = 2x + 2}}](https://tex.z-dn.net/?f=%5Ctextbf%7BSolve%3A%7D%5C%5C%5C%5C%5Ctext%7BUse%20the%20point-slope%20formula%20to%20solve.%7D%5C%5C%5C%5Cy%20-%20y1%20%3D%20m%28x%20-%20x1%29%5Cquad%7B%7D%5C%5C%5C%5C%5Ctext%7BPlug%20in%202%20to%20m%2C%201%20to%20x1%2C%204%20to%20y1%20and%20then%20solve.%7D%5C%5C%5C%5Cy%20-%204%20%3D%202%28x%20-%201%29%5C%5C%5C%5C%5Ctext%7BUse%20the%20%5Cunderline%7Bdistributive%20property%7D%20to%20distribute%20the%202.%7D%5C%5C%5C%5Cy%20-%204%20%3D%202x%20-%202%5C%5C%5C%5C%5Ctext%7BAdd%204%20to%20both%20sides%20to%20cancel%20the%204%20on%20the%20left%20and%20move%20the%20remainder%7D%5C%5C%5Ctext%7Bto%20the%20right%20side%20of%20the%20equal%20sign.%7D%5C%5C%5C%5Cy%20%3D%202x%20%2B%202%5C%5C%5C%5C%5Ctext%7BSince%20we%20can%27t%20simplify%20any%20further%2C%20our%20answer%20is%3A%20%5Cfbox%7By%20%3D%202x%20%2B%202%7D%7D)
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![\textbf{Answer:}\\\\\text{Therefore, the equation of the line (our final answer) would be \fbox{y = 2x + 2}}](https://tex.z-dn.net/?f=%5Ctextbf%7BAnswer%3A%7D%5C%5C%5C%5C%5Ctext%7BTherefore%2C%20the%20equation%20of%20the%20line%20%28our%20final%20answer%29%20would%20be%20%5Cfbox%7By%20%3D%202x%20%2B%202%7D%7D)
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Answer:
I need free points but all ik is the -4 needs to be divided by 4 then u have 5g+14=5g/-1
Step-by-step explanation:
The standard form:
![Ax+By=C](https://tex.z-dn.net/?f=Ax%2BBy%3DC)
The point-slope form:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
m - slope
(x₁, y₁) - point
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We have the points (2, -3) and (4, 2). Substitute:
![m=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B2-%28-3%29%7D%7B4-2%7D%3D%5Cdfrac%7B5%7D%7B2%7D)
![y-(-3)=\dfrac{5}{2}(x-2)](https://tex.z-dn.net/?f=y-%28-3%29%3D%5Cdfrac%7B5%7D%7B2%7D%28x-2%29)
<em>use distributive property</em>
<em>multiply both sides by 2</em>
<em>subtract 6 from both sides</em>
<em>subtract 5x from both sides</em>
<em>change the signs</em>
![\boxed{5x-2y=16}](https://tex.z-dn.net/?f=%5Cboxed%7B5x-2y%3D16%7D)