Question 203835
Write the slope-intercept equation of the line that is parallel to: -3x-5y=6 and has the same y-intercept as the graph of:  2x+y=-4


Ok, first we have to write a line that is parallel to -3x - 5y = 6.   What you have to know is that parallel lines have the SAME slope.  So, we just have to find the slope of this line:   -3x - 5y = 6.   How do we do that?  Let's solve this equation for y and in doing so, we'll put the equation in slope/intercept form.  The slope intercept form is y = mx + b. In this form, the "m" is the slope.  So, let's go.......


First we solve for y:


-3x - 5y = 6  (add 3x to both sides)
-5y = 3x + 6 (now divide both sides by -5 to isolate the y)

{{{(-5)y/-5 = (3x)/-5 + (6)/-5}}}


y = {{{(-3x)/5 - (6)/5}}}


Now can you see that your slope for the line is {{{-3/5}}}?   Therefore, our next line that we create has to have this for a slope if the two lines are going to end up being parallel.


Now the next part of your problem says:  the line must have the same y-intercept as the graph of, 2x + y = -4.    Hmmmm... What is the y intercept of this line?   Here's something for you to know:


To find the y intercept, solve for y by making x = 0.
To find the x intercept, solve for x by making y = 0.


SO in our equation:  2x + y = -4 
We just need to solve for y by making x = 0. Let's try it:


2x + y = -4 (original equation)
2(0) + y = -4
0 + y = -4
y = -4


SO we know that when x = 0, then y = -4.   Our y intercept is -4.



Now what do we want?  We want a line in the slope/intercept form (y = mx + b) and remember, that "m" is the slope.  What you also have to know is that "b" is the y intercept.  We want this new equation of a line to be parallel to the first line -3x - 5y = 6, which means the 2nd line must have (as we know from above) a slope of {{{-3/5}}}.


SO let's plug in our info to the equation of:

 y = mx + b
 y = {{{(-3)/(5)}}}x - 4


Do you see how we "plugged in" the value for m, which was {{{-3/5}}} as well as the value for "b" which was -4?


Does that make sense for you?  I hope so. :-)