Question

what is the slope of a line perpendicular to y=-2/3x+10 ? explain reasoning

Answer 1

the slope of a line perpendicular to another line of slope m
has slope -1/m.
in this case slope = -1 / (-2/3) = 3/2

Answer 2

in any line perpendicular, it would be the negative reciprocal of the slope in the other line. so for a live perp. to (a/b)x+c, the slope would be -b/a. in this case, it would be 3/2

Answer 3

The "reasoning" is that the tangent (slope or angle that a line makes with the positive x-axis has 90 degrees added or subtracted from it, changing the sign.