Question

Use the given conditions to write an equation for the line in point-slope form, in slope-intercept form and in standard form:
Passing through (5-4) and perpendicular to the line whise equation is 2x-3y=4

Answer 1

If the line perpendicular to 2x-3y=4 then it's equation is 3x + 2y + D = 0, where D is some constant. As the line passing through (5, -4) then 3*5 +2*(-4) +D = 0 => D = -7.
And we have forms 3x+2y-7=0, y = -3/2x + 7/2, (y +4) = -3/2(x - 3)