Respuesta :
Answer:
The correct answer is y - (-1)= 2/3(x - (-6))
Step-by-step explanation:
I know there was some confusion as to weather this answer was correct. But i an tell you that i am on FLVS and this was the correct answer to this problem.
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To solve the problem we will use the property of parallelogram.
What is a Parallelogram?
A parallelogram is a quadrilateral whose opposite sides are parallel to each other and equal in size.
The equation of the line WZ is [tex]y-(-1) = \dfrac{2}{3}[x -(-6)][/tex].
Given to us
- Randolph is creating parallelogram WXYZ,
- XY has an equation of y = 2 over 3x −5
- WZ must pass through the point (−6, −1)
Slope of the Line WZ
As we know for a parallelogram opposite sides must be parallel, therefore, line XY and WZ should be parallel to form a quadrilateral.
Thus, the slope of both the lines will be equal to each other.
Writing the equation of line for WZ
[tex]y = mx+c\\y = \dfrac{2}{3}x + c[/tex]
Value of Constant for equation of line WZ
As the line WZ passes through the point (-6, -1), therefore, substituting the given point to find the value of constant,
[tex]-1 = \dfrac{2}{3}(-6) + c\\\\-1 = 2(-2) + c\\\\-1 = -4 +c\\\\-1+4 =c\\\\c = 3[/tex]
Equation of the line WZ
[tex]y = \dfrac{2}{3}x + 3[/tex]
Adding +1, -1 on the right side of the equation,
[tex]y = \dfrac{2}{3}x + 3-1+1\\\\y+1=\dfrac{2}{3}x + 3+1\\\\y+1=\dfrac{2}{3}x + 4[/tex]
Taking [tex]\frac{2}{3}[/tex] as common,
[tex]y-(-1) = \dfrac{2}{3}(x +6)\\\\y-(-1) = \dfrac{2}{3}[x -(-6)][/tex]
Hence, the equation of the line WZ is [tex]y-(-1) = \dfrac{2}{3}[x -(-6)][/tex].
Learn more about Parallelogram:
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