Question 65946
Write the equation of the line whose y-intercept is (0, 2) and which is perpendicular to the line with equation: {{{2x-3y = 6}}}.
You can write the equation in the slope-intercept form. y = mx+b
You are given the y-intercept: b = 2
The slope can be found from the fact that it is perpendicular to 2x-3y = 6
Find the slope of the given line by rewriting it in the slope-intercept form.
{{{2x-3y = 6}}} Add 3y to both sides.
{{{2x = 3y+6}}} Subtract 6 from both sides.
{{{2x-6 = 3y}}}  Divide both sides by 3.
{{{(2/3)x-2 = y}}} or
{{{y = (2/3)x-2}}} Compare this with:
{{{y = mx+b}}} The slope of the given line is m = 2/3
A line that is perpendicular to this will have a slope that is the negative reciprocal of {{{2/3}}}, so the slope of the new line is {{{m = -3/2}}}.
The equation of the new line is:
{{{y =-(3/2)x+2}}}