Question 805791
{{{highlight(x/5+y/(-3)=1)}}} is the fastest answer.
You could call that the intercepts form of the equation for the line.
If a line passes through points (a, 0) and (0, b), its x- and y-intercepts,
then {{{x/a+y/b=1}}} is an equation that represents the line.
You may have been taught such a form, with that name or another name
Since some people do not like denominators, I could multiply both sides of the equal sign times 15 to get
{{{highlight(3x-5y=15)}}}
Multiplying times other factors you can get a variety of answers.
You can also solve for y to get the unique equation in slope intercept form
{{{15=3x-5y}}}-->{{{5y=3x-15}}}-->{{{highlight(y=(3/5)x-3)}}}
If you had not been shown the fact that
"if a line passes through points (a, 0) and (0, b), its x- and y-intercepts,
{{{x/a+y/b=1}}} is an equation that represents the line,"
then you could easily write a system of equations by plugging in the coordinates of those intercepts into {{{y=mx+b}}} .
Solving the system would get you {{{m}}} and {{{b}}} , and then you could write the equation in the {{{y=mx+b}}} form.
{{{system(-3=m*0+b,0=m*5+b)}}}-->{{{system(b=-3,5m-3=0)}}}-->{{{system(b=-3,5m=3)}}}-->{{{highlight(system(b=-3,m=3/5))}}}