Find the equation of the line perpendicular to y=-2/3x -7 that runs through the points (6,1) in slope intercept form

The equation of line is:[tex]y = \frac{3}{2}x-8[/tex]Further explanation:Given equation of line[tex]y=-\frac{2}{3}x-7[/tex]Comparing it with the standard formy = mx + b gives us:slope = m1 = -2/3Let m2 be the slope of second lineThe product of slopes of two perpendicular lines is -1.[tex]m_1* m_2 = -1\\-\frac{2}{3} *m_2 = -1\\m_2 = -1 * -\frac{3}{2}\\m_2 = \frac{3}{2}\\Putting\ in\ standard\ form\\y = \frac{3}{2}x +b[/tex]We have to find the value of b. So, Putting the point(6,1)[tex]1 = \frac{3}{2}(6) +b\\1 = (3 * 3) + b\\1=9+b\\1-9 =b\\b = -8\\The\ final\ equation\ is:\\y= \frac{3}{2}x -8[/tex]Keywords: Coordinate geometry, Point-slope formLearn more about coordinate geometry at:brainly.com/question/2488474brainly.com/question/2601054#LearnwithBrainly