Answer:
y=
4
3
x−22
Step-by-step explanation:
We are given;
The equation of a line 6x-2y=4+6y
A point (8, -16)
We are required to determine the equation of a line parallel to the given line and passing through the given point.
One way we can determine the equation of a line is when we are given its slope and a point where it is passing through,
First we get the slope of the line from the equation given;
We write the equation in the form y = mx + c, where m is the slope
That is;
6x-2y=4+6y
6y + 2y = 6x-4
8y = 6x -4
We get, y = 3/4 x - 4
Therefore, the slope, m₁ = 3/4
But; for parallel lines m₁=m₂
Therefore, the slope of the line in question, m₂ = 3/4
To get the equation of the line;
We take a point (x, y) and the point (8, -16) together with the slope;
That is;
\frac{(y--16}{x-8}=\frac{3}{4}
x−8
(y−−16
=
4
3
\begin{gathered}4(y+16)=3(x-8)\\4y + 64 = 3x - 24\\4y=3x-88\\ y=\frac{3}{4}x-22\end{gathered}
4(y+16)=3(x−8)
4y+64=3x−24
4y=3x−88
y=
4
3
x−22
Thus, the equation required is y=\frac{3}{4}x-22y=
4
3
x−22
