Rise over run is another term for slope, with we can use to derive a linear equation.
The term rise over run in technical terms is the change of y over the change of x.
To find the rise over run, subtract the y terms and divide that by the x terms.
![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
You can use this to derive a linear equation as earlier mentioned by plugging in given points.
For example, a line passes through (3,4) with a rise over run of 3.
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
![4=3(3)+b](https://tex.z-dn.net/?f=4%3D3%283%29%2Bb)
![4=9+b](https://tex.z-dn.net/?f=4%3D9%2Bb)
![b=-5](https://tex.z-dn.net/?f=b%3D-5)
So therefore the y intercept is -5, and the equation is ![y=3x-5](https://tex.z-dn.net/?f=y%3D3x-5)
Answer:
X=(6x+1)(x-1) because you are factoring out
For 7, when GH=HI, that means mG=mI so mI is 55
for 8, mJ would equal 58 since 180-122 is 58. 58+67 is 125 and 180 - 125 is 55, so mk is 55
Answer:
The value that maximize the objective function is the point (1,4)
Step-by-step explanation:
we have
----> inequality A
----> inequality B
----> inequality C
----> inequality D
Using a graphing tool
The solution is the shaded area
see the attached figure
The coordinates of the solution area are
![(0,0),(0,4.5),(1,4),(2.33,0)](https://tex.z-dn.net/?f=%280%2C0%29%2C%280%2C4.5%29%2C%281%2C4%29%2C%282.33%2C0%29)
we have
The Objective Function is equal to
![P=2x+y](https://tex.z-dn.net/?f=P%3D2x%2By)
To find out the value of x and y that maximize the objective function, substitute each ordered pair of the vertices in the objective function and then compare the results
For (0,0) --------> ![P=2(0)+0=0](https://tex.z-dn.net/?f=P%3D2%280%29%2B0%3D0)
For (0,4.5) --------> ![P=2(0)+4.5=4.5](https://tex.z-dn.net/?f=P%3D2%280%29%2B4.5%3D4.5)
For (1,4) --------> ![P=2(1)+4=6](https://tex.z-dn.net/?f=P%3D2%281%29%2B4%3D6)
For (2.33,0) --------> ![P=2(2.33)+0=4.66](https://tex.z-dn.net/?f=P%3D2%282.33%29%2B0%3D4.66)
The value that maximize the objective function is the point (1,4)
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