Answer:
![x=-1](https://tex.z-dn.net/?f=x%3D-1)
Step-by-step explanation:
![4=6+2x](https://tex.z-dn.net/?f=4%3D6%2B2x)
Flip the equation:
![2x+6=4](https://tex.z-dn.net/?f=2x%2B6%3D4)
Subtract 6 from both sides:
![3x+6-6=4-6](https://tex.z-dn.net/?f=3x%2B6-6%3D4-6)
![2x=-2](https://tex.z-dn.net/?f=2x%3D-2)
Divide both sides by 2:
![2x/2=-2/2](https://tex.z-dn.net/?f=2x%2F2%3D-2%2F2)
![x=-1](https://tex.z-dn.net/?f=x%3D-1)
Answer:
a.![y=2x](https://tex.z-dn.net/?f=y%3D2x)
b.![y=2x+3](https://tex.z-dn.net/?f=y%3D2x%2B3)
Step-by-step explanation:
We are given that a line
![y=x](https://tex.z-dn.net/?f=y%3Dx)
a. We have to find the equation of resulting line when the given line is dilated by a factor of 2.
We know that when a line is dilated by a then equation of line is given by
![y=ax](https://tex.z-dn.net/?f=y%3Dax)
We have a=2
Then, equation of line after dilation
![y=2x](https://tex.z-dn.net/?f=y%3D2x)
b.We have to find the equation of line when resulting line is translated 3 units up
Transformation rule when the y shift 3 units upward is given by
![(x,y)\righarrow (x,y+3)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crigharrow%20%28x%2Cy%2B3%29)
When the line
is translated 3 units up then the equation of line is given by
![y=2x+3](https://tex.z-dn.net/?f=y%3D2x%2B3)
A = 2
b = 2
c = -4
"a" is greater than zero so the vertex is a minimum point and the graph is concave up.
The (x,y) point of the vertex is usually designated by the letters (h, k)
The "x" position (or "h") is calculated with this formula:
h = -b / 2a
h = -2 / 4
h = -1 / 2
"k" is calculated with this equation:
k = ah^2 + bh +c
k =(2*-1 / 2 * -1 / 2) + (2 * -1 / 2) + -4
k = (1 / 2) - 1 -4
k = -4.5
so the vertex is at point (-.5, -4.5)
Source:
http://www.1728.org/quadr3.htm