Write the equation of the line perpendicular to 2x+3y=9 that passes through (-2,5). write your answer in slope-intercept form. show work .

First find the slope of the first line. The line is in standard form, Ax + By = C, and slope is given by -A/B. Therefore, the slope of 2x+3y=9 is -2/3.

Now, if lines are perpendicular, their slopes are the negative reciprocals of each other. So, the slope of the line you want to find is the reciprocal of -2/3  (-3/2) multiplied by -1, or 3/2.

To find the equation of the line, we can use point-slope form because we have a point (-2, 5), and a slope that we calculated (3/2). Point-slope form is y-y₁=m(x-x₁) where (x₁, y₁) is a point and m is the slope. Our point is (-2, 5) so x₁ = -2 and y₁ = 5. Our slope is 3/2. Now, simply plug the values into the formula: y-5=3/2(x-(-2)). To convert the equation from point slope form to slope-intercept form, simply isolate y and get rid of parenthesis by distributing.

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