Question 281612
You have to get the equation into the
form {{{y = mx + b}}}, where {{{m}}} = slope
{{{4y - 5 = 2x}}}
Add {{{5}}} to both sides
{{{4y = 2x + 5}}}
divide both sides by {{{4}}}
{{{y = (1/2)*x + 5/4}}}
Any line parallel to this line will have slope = {{{1/2}}}
So far I have {{{y = (1/2)*x + b}}}, and all I need is {{{b}}}
The line must pass through (-3,-2), so I can just plug
these values in and solve for {{{b}}}
{{{-2 = (1/2)*(-3) + b}}}
Multiply both sides by {{{2}}}
{{{-4 = -3 + 2b}}}
Add {{{6}}} to both sides
{{{2b = -1}}}
{{{b = -1/2}}}
The solution is {{{y = (1/2)*x - 1/2}}}
check:
does it go through (-3,-2)?
{{{-2 = (1/2)*(-3) - 1/2}}}
{{{-2 = -3/2 - 1/2}}}
{{{-2 = -2}}}
OK