SOLUTION: A line parallel to 3x-9y=4 and sketch the graph

Question 53664This question is from textbook
: A line parallel to 3x-9y=4 and sketch the graph This question is from textbook

Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
Is there a point you're supposed to go through. Usually books the line to go through a specific point. Since you didn't give me a point, I'm going to have my parallel line go through the origin (0,0) because it's the easiest point I can think of. If you were supposed to use another point let me know and I'll change it.
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Parallel lines have the same slopes (m).
To find the slope of the line that you gave me, weput the line in slope intercept form: y=mx+b. m=slope and (0,b)= y-itnercept.
3x-9y=4
-3x+3x-9y=-3x+4
-9y=-3x+4
-9y/-9=-3x/-9+4/-9
y=1/3x-4/9
The slope of this line: m=1/3.
Therefore, the slope of a line that is parallel to this line is also m=1/3.
We're going through the point (0,0) so are new (0,b)=(0,0).
Write the equation in y=mx+b form and you have:
y=1/3x+0
y=1/3x
You can graph the first line by plotting (0,-4/9) and then use the slope=rise/run=1/3. Go up 1 and right 3 plot a point at (3,5/9).
Graph the second line by plotting (0,0) and then go up1 and right 3 and plot your second point at (3,1).
The red one is the line you gave me and the green one is parallel to it. Parrallel lines can go on forever and ever and never touch because they have the exact same slant.

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