SOLUTION: Determine the equation of the line which is parallel to the line 4x - 5y = 9 and has the same y intercept as the line (2x) / 3 + (4y) / 5 = 8 I don't know how to do this. Tha

Algebra ->  Graphs -> SOLUTION: Determine the equation of the line which is parallel to the line 4x - 5y = 9 and has the same y intercept as the line (2x) / 3 + (4y) / 5 = 8 I don't know how to do this. Tha      Log On


   

Question 548266: Determine the equation of the line which is parallel to the line 4x - 5y = 9 and has the same y intercept as the line (2x) / 3 + (4y) / 5 = 8
I don't know how to do this.
Thank you
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
Let's look at the first part:
Determine the equation of the line which is parallel to the line 4x - 5y = 9
We know that parallel lines have the same slope (m value)
We can rearrange this formula into y=mx+b and find that m-value.
4x-5y=9
4x-5y%2B5y-9=9%2B5y-9
4x-9=5y
%284x-9%29%2F5=5y%2F5
%284x-9%29%2F5=y
y=%284%2F5%29%2Ax-9%2F5
So the m value is 4/5

For the second part,
Again we can rearrange (2x) / 3 + (4y) / 5 = 8 into y=mx+b form and the b value will be the y-intercept

%282x%29+%2F+3+%2B+%284y%29+%2F+5+=+8
Multiple every term by 3
3%2A%28%282x%29+%2F+3%29+%2B+3%2A%28%284y%29+%2F+5%29+=+3%2A8
%282x%29+%2B+%28%2812y%29+%2F+5%29+=+24
Now multiply every term by 5
5%2A%282x%29+%2B+5%2A%28%2812y%29+%2F+5%29+=+5%2A24
%2810x%29+%2B+%2812y%29+=+120
%2810x%29+%2B+%2812y%29+-10x=+120-10x
12y=+120-10x
12y%2F12=+120%2F12-10x%2F12
y=+10-10%2F12%2Ax
y=-10%2F12%2Ax%2B10
From this we see that the b-value is 10



Since the line we are looking for has the same slope and same y-intercept, we can plug these values right into the y-intercept form of a line (y=mx+b). This leaves:
y=4%2F5%2Ax%2B10

Hopefully this helps:)