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what is the equation in slope intercept form of the line that goes through (2,4) and is perpendicular to the line represented by y=-2/3x+6

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Answer:


y = (3x)/(2)+1

Explanation:

The slope-intercept form of a straight line equation is y = mx + c, where m is the slope and c is the y-intercept of the line.

Now, we know that if two straight lines are perpendicular to each other then the product of their slopes will be -1.

So, the equation of a straight line which is perpendicular to the line
y = -(2x)/(3) +6 will be
y= (3x)/(2)+ c' ....... (1), where c' is constant.

Given that the line (1) passes through (2,4) point.

Hence,
4 = (3(2))/(2) +c'

c' = 1.

Therefore, the final equation of the required straight line is
y = (3x)/(2)+1. (Answer)

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