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Part 1
Find an equation for the line with the given properties. Express your answer using either the general form or the​ slope-intercept form of the equation of a line.
Perpendicular to the line y=
1
2x−2​; containing the point ​(−3​,6​)

The equation of the line  in slope-intercept form is y = -x/12 + 23/4How to find the equation of the line?Given that: the line is perpendicular to the line y= 12x−2 and it contains the ​(−3​,6​).The slope-intercept form of a straight line is: y = mx + c, where m is the slope and c is the y-interceptWhen the two lines are perpendicular, the product of their slope is -1 i.e.m1 x m2 = -1where m1 and m2 represent the slope of the linesLet the slope of the given line be m1 and the slope of the unknown line be m2Line1(given): y = 12x−2   and m1 = 12m1 x m2 = -112 x m2 = -1m2 = -1/12Line 2(unknown) with the point ​(−3​,6​):y = mx + c6 = -1/12 (-3) + c6 = 1/4 + cc = 6 -1/4 = 23/4y = -x/12 + 23/4Therefore, the slope-intercept form of the equation of the line is y = -x/12 + 23/4Learn more about equation of a line on:https://brainly.com/question/12626026#SPJ1