1. In slope-intercept form, write an equation of a line that passes through $(4,25)$ and is perpendicular to the line $y=\frac{2}{5} x+6$
\[
y=
\]
$\sqrt{x}$.

Step 1 ：The slope-intercept form of a line is given by \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.

Step 2 ：The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.

Step 3 ：The slope of the given line is \(\frac{2}{5}\), so the slope of the line perpendicular to it is \(-\frac{5}{2}\).

Step 4 ：We can use the point-slope form of a line, \(y - y_1 = m(x - x_1)\), to find the equation of the line. Here, \((x_1, y_1)\) is the point \((4, 25)\).

Step 5 ：Substituting the values, we get \(m = -2.5\) and \(c = 35.0\).

Step 6 ：The equation of the line that passes through \((4,25)\) and is perpendicular to the line \(y=\frac{2}{5} x+6\) is \(y=-\frac{5}{2}x+35\).

Step 7 ：Final Answer: \(\boxed{y=-\frac{5}{2}x+35}\)