Answer:
To find the equation of a line that is perpendicular to the given line \(y = 5x - 19\) and passes through the point (3, 4), we can use the point-slope form of the equation for a line:
\(y - y_1 = m(x - x_1)\),
where \((x_1, y_1)\) is the given point, and \(m\) is the slope of the line.
The slope of the line \(y = 5x - 19\) is \(m = 5\). Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the perpendicular line will be \(-1/5\).
Using the point-slope form with the point (3, 4) and the slope \(-1/5\):
\(y - 4 = -1/5(x - 3)\).
Now, we can rearrange this equation into a more familiar form, if desired:
\(y - 4 = -1/5x + 3/5\),
\(y = -1/5x + 3/5 + 4\),
\(y = -1/5x + 23/5\).
So, the equation of the line that is perpendicular to \(y = 5x - 19\) and passes through the point (3, 4) is \(y = -1/5x + 23/5\).
Explanation: