Question 526373
Write the equation for the line: with y-intercept -1 and perpendicular to 3x-2y=6.
.
y = mx + b
y = mx -1 will have a y-intercept of (0,-1)
.
Get 3x -2y = 6 into slope-intercept form.
.
3x -2y = 6
-2y = -3x +6
y = 3/2*x +3
.
The line perpendicular to this line will have a slope that is the inverse reciprocal of m = 3/2
which is -2/3 and b = -1.
.
y = -2/3*x -1
.
y-intercept = (0,-1)
x-intercept = the point where y  = 0.  So set y=0 and solve for x.
0 = -2/3*x -1
2/3*x = -1
2x = -3
x = -3/2
(-3/2, 0)
.
In the following graph:
the red line is y = 3/2*x +3
the green line is y = -2/3*x -1
.
{{{ graph(500,500,-5,5,-5,5,3/2*x+3,-2/3*x-1) }}}
.
Looking back at the question, it asks for the equation in standard form.
.
y = -2/3*x -1
multiply by 3 to eliminate fraction
3y = -2x -3
add 2x to both sides
2x +3y = -3
.
Done.