Answer:
The equation \(y = 4x - 2\) represents a line with a slope of 4 (since the
coefficient of \(x\) is 4).
For a line parallel to \(y = 4x - 2\), it should have the same slope as 4. Lines that are parallel have the same slope but different y-intercepts.
Now, using the point-slope form of a line (\(y - y_1 = m(x - x_1)\)) where \((x_1, y_1)\) is the given point (8, 4) and \(m\) is the slope (4):
\(y - 4 = 4 \cdot (x - 8)\)
\(y - 4 = 4x - 32\)
Now, solve for \(y\):
\(y = 4x - 32 + 4\)
\(y = 4x - 28\)
Therefore, the equation of the line parallel to \(y = 4x - 2\) and passing through the point (8, 4) is \(y = 4x - 28\).
Explanation: