Help fast please! Will give brainliest!Find the equation in slope-intercept form of the line that is the perpendicular bisector of thesegment between (-3, 2) and (3, -8). Please show work.

The equation in slope-intercept form of the line that is the perpendicular bisector of the  segment between (-3, 2) and (3, -8) is:[tex]y=\frac{3}{5}x-3[/tex]Step-by-step explanation:As the required line is perpendicular bisector of the given line segment, it will pass through the mid-point of the given line segment.(x1,y1) = (-3,2)(x2,y2) = (3,-8)so,[tex]Mid-point = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\\=(\frac{-3+3}{2}, \frac{2-8}{2})\\=(\frac{0}{2},\frac{-6}{2})\\=(0, -3)[/tex]We also have to find the slope of the required lineLet m1 be the slope of given line and m2 be the slope of required lineso,[tex]m_1 = \frac{y_2-y_1}{x_2-x_1}\\=\frac{-8-2}{3+3}\\=\frac{-10}{6}\\=-\frac{5}{3}[/tex]The product of slopes of two perpendicular lines is -1, So[tex]-\frac{5}{3}*m_2=-1\\m_2=-1 * -\frac{3}{5}\\m_2=\frac{3}{5}[/tex]Slope-intercept form is:[tex]y=m_2x+b[/tex]Putting the value of m2[tex]y=\frac{3}{5}x+b[/tex]As the line passes through (0,-3)[tex]-3=\frac{3}{5}*0 + b\\-3=b[/tex]So.,The equation in slope-intercept form of the line that is the perpendicular bisector of the  segment between (-3, 2) and (3, -8) is:[tex]y=\frac{3}{5}x-3[/tex]Keywords: Slope-intercept form, SlopeLearn more about equation of line at:brainly.com/question/4021035brainly.com/question/4034547#LearnwithBrainly