Answer
The slope of a line perpendicular to the given line $-\frac{2}{5}$.
Work Step by Step
RECALL:
$\\\\$(i) The slope-intercept form of a line's equation is y=mx+b, m=slope and b=y-intercept.
$\\\\$(ii) Perpendicular lines have slopes that are negative reciprocals of each other (product of -1).
$\\\\$Write the given equation in slope-intercept form to have:
$\\\\-2y=-5x+6
\\\\y=\dfrac{-5x+6}{-2}
\\\\y=\frac{5}{2}x-3$
$\\\\$The given function has a slope of $\frac{5}{2}$.
$\\\\$Perpendicular lines have slopes that are negative reciprocals of each other.
$\\\\$Therefore, the slope of a line perpendicular to the given line $-\frac{2}{5}$.
