Equation of line passing through (2, -2) and parallel to 2x+3y = -8 is ![y=\frac{-2 x}{3}+\frac{-2}{3}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-2%20x%7D%7B3%7D%2B%5Cfrac%7B-2%7D%7B3%7D)
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Solution:</u></h3>
Need to write equation of line parallel to 2x+3y=-8 and passes through the point (2, -2)
Generic slope intercept form of a line is given by y = mx + c
where "m" = slope of the line and "c" is the y - intercept
Let’s first find slope intercept form of 2x+3y=-8 to get slope of line
![\begin{array}{l}{2 x+3 y=-8} \\\\ {=>y=\frac{-2 x-8}{3}} \\\\ {\Rightarrow y=-\frac{2}{3} x-\frac{8}{3}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B2%20x%2B3%20y%3D-8%7D%20%5C%5C%5C%5C%20%7B%3D%3Ey%3D%5Cfrac%7B-2%20x-8%7D%7B3%7D%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20y%3D-%5Cfrac%7B2%7D%7B3%7D%20x-%5Cfrac%7B8%7D%7B3%7D%7D%5Cend%7Barray%7D)
On comparing above slope intercept form of given equation with generic slope intercept form y = mx + c,
![\text {for line } 2 x+3 y=-8, \text { slope } m=-\frac{2}{3}](https://tex.z-dn.net/?f=%5Ctext%20%7Bfor%20line%20%7D%202%20x%2B3%20y%3D-8%2C%20%5Ctext%20%7B%20slope%20%7D%20m%3D-%5Cfrac%7B2%7D%7B3%7D)
We know that slopes of parallel lines are always equal
So the slope of line passing through (2, -2) is also ![m=-\frac{2}{3}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B2%7D%7B3%7D)
Equation of line passing through
and having slope of m is given by
![\left(y-y_{1}\right)=\mathrm{m}\left(x-x_{1}\right)](https://tex.z-dn.net/?f=%5Cleft%28y-y_%7B1%7D%5Cright%29%3D%5Cmathrm%7Bm%7D%5Cleft%28x-x_%7B1%7D%5Cright%29)
![\text { In our case } x_{1}=2 \text { and } y_{1}=-2](https://tex.z-dn.net/?f=%5Ctext%20%7B%20In%20our%20case%20%7D%20x_%7B1%7D%3D2%20%5Ctext%20%7B%20and%20%7D%20y_%7B1%7D%3D-2)
Substituting the values in equation of line we get
![(y-(-2))=-\frac{2}{3}(x-2)](https://tex.z-dn.net/?f=%28y-%28-2%29%29%3D-%5Cfrac%7B2%7D%7B3%7D%28x-2%29)
![\begin{array}{l}{\Rightarrow y+2=\frac{-2 x+4}{3}} \\\\ {=>3(y+2)=-2 x+4} \\\\ {=>3 y+6=-2 x+4} \\\\ {3 y=-2 x-2}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5CRightarrow%20y%2B2%3D%5Cfrac%7B-2%20x%2B4%7D%7B3%7D%7D%20%5C%5C%5C%5C%20%7B%3D%3E3%28y%2B2%29%3D-2%20x%2B4%7D%20%5C%5C%5C%5C%20%7B%3D%3E3%20y%2B6%3D-2%20x%2B4%7D%20%5C%5C%5C%5C%20%7B3%20y%3D-2%20x-2%7D%5Cend%7Barray%7D)
![y=\frac{-2 x}{3}+\frac{-2}{3}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-2%20x%7D%7B3%7D%2B%5Cfrac%7B-2%7D%7B3%7D)
Hence equation of line passing through (2 , -2) and parallel to 2x + 3y = -8 is given as ![y=\frac{-2 x}{3}+\frac{-2}{3}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-2%20x%7D%7B3%7D%2B%5Cfrac%7B-2%7D%7B3%7D)
Answer:
C = 6.28 ft
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d where d is the diameter
C = 3.14(2)
C = 6.28 ft
Answer: QE = 10
Step-by-step explanation: To solve this problem, it's important to understand that the diagonals of a parallelogram bisect each other.
This means that E is the midpoint of diagonal SQ.
So we can setup the equation x² + 9x = 4x + 6.
To solve this polynomial equation, set it equal to zero first.
So we have x² + 5x - 6 = 0 and we get (x + 6)(x - 1) = 0
when we factor the left side of the equation.
So this means that x = -6 or x = 1.
However, -6 will give us a negative length when we plug it in
to find QE so this will not work.
However, plugging 1 in will give us 10 as a length so QE = 10.
The correct answer is A. x=22
Since the angles of a rectangle are right angles (90 degrees) you would set it up as 90=5x-20. Then combine like terms and solve the equation. (If you need me to show you how step by step tell me)
Yes <span>-(12/-17) is equal to 12/17
I hope this helps.
Have a awesome day. :)</span>