What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ?Enter your answer in the box.

Answer:[tex]\frac{2}{3}[/tex] is the Slope of a line that is perpendicular to a given line equation -2y=3x+7 Step-by-step explanation:We are given here with the equation of the line [tex]-2y=3x+7[/tex] or we can write this equation as [tex]y=\frac{-3}{2}x+\frac{-7}{2}[/tex] the general equation of the line [tex]y=mx+b[/tex]  where m is the slope and b is the y-intercept.Compare the given equation with general equation we get, the value of  slope(m) [tex]=\frac{-3}{2}[/tex]The slope of line perpendicular to a line is, [tex]m_{perpendicular}=\frac{-1}{m}[/tex]Since, the slope of the given line is, m=[tex]\frac{-3}{2}[/tex]then, [tex]m_{perpendicular}=\frac{-1}{\frac{-3}{2} }[/tex][tex]=\frac{2}{3}[/tex]Therefore, the slope of a line that is perpendicular to a line whose equation is -2y=3x+7 is, [tex]\frac{2}{3}[/tex]