Question 186467
Call the x-intercept {{{x[i]}}}
Call the y-intercept {{{y[i]}}}
Call the slope {{{m}}}
{{{(1/2)*x[i]y[i] = 24}}}
{{{x[i]y[i] = 48}}}
{{{y[i] = 48/x[i]}}}
and
{{{m = -(y[i]/x[i])}}}
{{{m = - (48/(x[i])^2)}}}
The general equation is
{{{y = mx + b}}} and goes through (3,4)
and {{{b}}} is the y-intercept
{{{4 = m*3 + b}}}
{{{4 = 3m + y[i]}}}
{{{4 = -3*(48/(x[i])^2) + y[i]}}}
{{{4 = -3*(48/(x[i])^2) + 48/x[i]}}}
{{{4*(x[i])^2 = -144 + 48x[i]}}}
{{{4*(x[i])^2 - 48x[i] + 144 = 0}}}
{{{(x[i])^2 - 12x[i] + 36 = 0}}}
{{{(x[i] - 6)^2 = 0}}}
{{{x[i] = 6}}}
The x-intercept is {{{6}}} answer
and
{{{y[i] = 48/x[i]}}}
{{{y[i] = 48/6}}}
{{{y[i] = 8}}}
check:
{{{(1/2)*x[i]y[i] = 24}}}
{{{(1/2)*6*8 = 24}}}
{{{24 = 24}}}
{{{m = -(y[i]/x[i])}}}
{{{m = -(8/6)}}}
{{{m = -(4/3)}}}
The general equation is:
{{{y = -(4/3)*x + 8}}}
does it go through (3,4)?
{{{4 = -(4/3)*3 + 8}}}
{{{4 = -4 + 8}}}
{{{4 = 4}}} 
OK