Get the equation of the line in point-slope form

Determine the equation of a line in point-slope form that passes through (3, -4) and is perpendicular
to the line -2x + 3y = -15.

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Get the given equation in slope-intercept form, y = mx + b.

-2x + 3y = -15
3y = 2x - 15 {added 2x to each side}
y = (2/3)x - 5 {divided each side by 3}
slope = 2/3

Perpendicular lines have slopes which are negative reciprocals of each other.

perpendicular slope is -3/2

slope is -3/2 and point is (3,-4)

Substitute point and slope into point-slope form.

y - y1 = m(x - x1) {point-slope form}
y - (-4) = (-3/2)(x - 3) {substituted into point-slope form}
y + 4 = (-3/2)(x - 3) {simplified double negative signs}

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