Question 73791
Write the equation of the line L satisfying the given geometric conditions.
L has y-intercept (0, 2) and is perpendicular to the line with equation 2x-3y=6.
Perpendicular lines have slopes that are negative reciprocals of each other (opposite signs and upside down), because of that if we multiply them we get -1.
The slope intecept form of a line is {{{highlight(y=mx+b)}}}, where m=slope and (0,b) is the y-intercept.
If we put the equation they gave you in y-intercept form we can determine its slope.
{{{2x-3y=6}}}
{{{-2x+2x-3y=-2x+6}}}
{{{-3y=-2x+6}}}
{{{-3y/-3=-2x/-3+6/-3}}}
{{{y=(2/3)x-2}}}  the slope, m=2/3
The slope of any line perpendicular to this one is: m=-3/2
Our line has a slope of m=-3/2 and a y-intercept of (0,b)=(0,2)
Plugging that into the slope intercept form y=mx+b, gives us:
{{{highlight(y=(-3/2)x+2)}}}
Happy Calculating!!!!