Answer
The slope of a line perpendicular to the given line $-\frac{4}{3}$.
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 (has a product of -1).
$\\\\$Write the given equation in slope-intercept form to have:
$\\\\4y=3x+10
\\\\y=\dfrac{3x+10}{4}
\\\\y=\frac{3}{4}x+\frac{5}{2}$
$\\\\$The given function has a slope of $\frac{3}{4}$.
$\\\\$Perpendicular lines have slopes that are negative reciprocals of each other.
$\\\\$Therefore, the slope of a line perpendicular to the given line $-\frac{4}{3}$.
