L has y-intercept (0, 2) and is perpendicular to the line with equation 2x – 3y = 6

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I'm guessing that you want the equation of the line L that has a y intercept of (0,2) that is also perpendicular to the line 2x + 3y = 6.First, find the slope of the second line. Solve the equation for y, which will make the equation look like slope-intercept form, making it really easy to determine the slope.2x + 3y = 62x + 3y - 2x = 6 - 2x3y = 6 - 2x(3y)/3 = (6 - 2x)/3y = 2 - (2/3)xthe slope is the coefficient of the x term, which is -2/3.the slope of a line perpendicular to this is the opposite reciprocal, which is 3/2.The line you are looking for has a slope of 3/2 and a y intercept of 2.The equation is y = (3/2)x + 2