Which equation in slope-intercept form represents a line that passes through the point (2,3) and is perpendicular to the line y−9=2/3(x+7)?

Answer 1

From the equation of the given line, the slope of this line is 2/3. A perpendicular line has a slope that is a negative reciprocal to this slope (flipped and opposite sign). Therefore, the slope of the newer line would be -3/2.

Using the point-slope equation with this slope of -3/2 and the point (2,3), we have: y-3=(-3/2)(x-2). If we distribute the slope through, this becomes y-3=(-3/2)x +3. If we add 3 to both sides to isolate "y", this becomes y = (-3/2)x +6.

Answer: y = (-3/2)x + 6