Question 934307
the equation of the line perpendicular to {{{2x-3y+7=0}}} and with the same x-intercept as {{{4x+5y-8=0}}}

first find x-intercept of {{{4x+5y-8=0}}}:

{{{4x+5y-8=0}}}...set {{{y=0}}} and solve for {{{x}}}

{{{4x+5*0-8=0}}}

{{{4x=8}}}

{{{x=8/4}}}

{{{x=2}}}

the x-intercept is at ({{{2}}},{{{0}}})

use this point and given line {{{2x-3y+7=0}}} in slope intercept form to find equation of perpendicular line which passes through ({{{2}}},{{{0}}}):

{{{2x+7=3y}}}

{{{y=(2/3)x+7/3}}}


*[invoke equation_parallel_or_perpendicular "perpendicular", "2/3", "7/3", 2, 0] 


so, the line {{{y=-(3/2)x+3}}}(green) is perpendicular to line {{{2x-3y+7=0}}}(red) and has same x-intercept as a line {{{4x+5y-8=0}}} (blue )

see all three on a graph:

{{{ graph( 600, 600, -10,10, -10, 10, (2/3)x+7/3, -(3/2)x+3,-4x/5+8/5) }}}