Question 250242
Let's take this a step at a time:

You want a line parallel to 2x+4y =9.  So the first thing you have to know is lines that are parallel have the SAME slope.  

Therefore, you have to find the slope for the equation, 2x + 4y = 9.  How can you do that?  


Let's change the equation to the y = mx + b format (the slope intercept form of a line) where "m" is the slope.  If we want to put the equation into y = mx + b format, we have to solve for "y".  SO here goes:


2x+ 4y = 9  (your original equation)
4y = -2x + 9  (subtracted 2x from both sides to isolate the y)

y = {{{-2x/4}}} + {{{9/4}}}  (divided both sides by 4 to isolate the y)


y = {{{-1/2x}}} + {{{9/4}}}  (simplified the fraction of {{{-2/4}}} to {{{-1/2}}})



Now we can see that the slope of the line is {{{-1/2}}}}.  Therefore, any line parallel to that line must ALSO have a slope of {{{-1/2}}}.


Now to the next step:


Your new line must also go thru the point   (6, -2)


When you know the point that a line must go thru and the slope you want, then you just "plug" this info into the point/slope form of a line.  The point slope form of a line is:


{{{(y - y[1])}}} = {{{m(x  - x[1])}}}



SO let's plug in our info:

We want a slope of {{{-1/2}}} and we want it to go thru point (6, -2)


y - -2 = {{{-1/2}}}(x - 6)  


y - -2 is really y + 2 so let's rewrite the above and then do the math.


y + 2 = {{{-1/2}}}(x - 6)  If your teacher wants the answer in "point/slope" form, you are finished at this step.  If the teacher wants the answer in slope/intercept form, then you have to do more thinking.  You'd have to do this:


y + 2 = {{{-1/2}}}(x - 6)  (equation in point/slope form)
y + 2 = {{{-1/2x}}} + 3   (distributed {{{-1/2}}})
y = {{{-1/2x}}} + 3 - 2 (subtracted 2 from both sides of the equation)

y = {{{-1/2x}}} + 1 (equation in slope intercept form)


I think that's everything.  I hope it helps you and good luck on your final. :-)