SOLUTION: What is the equation of the line through (0,9) that is parallel to the line 3x+5y=15?

Algebra ->  Linear-equations -> SOLUTION: What is the equation of the line through (0,9) that is parallel to the line 3x+5y=15?      Log On


   

Question 83081: What is the equation of the line through (0,9) that is parallel to the line 3x+5y=15?
Found 2 solutions by chitra, rapaljer:
Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
The given line equation is:

3x + 5y = 15


Writing this eqn in the form of y = mx + b, we get:


5y = -3x + 15

==> +y+=+-%283%2F5%29x+%2B+%2815%2F5%29

==> y+=+-%283%2F5%29x+%2B+3

From the above equation, we can find that the slope is given by, m = %28-3%2F5%29

Let the equation of the line parallel to the given line be in the form

y = mx + b. It will have the same slope as that of the given line. Also given that the point (0,9) passess through the given line. Hence,


y = %28-3%2F5%29x + b


9 = %28-3%2F5%29(0) + b

==> b = 9

Thus, the equation of the requied line is:

y = -%283%2F5%29 + 9


Hence, the solution.

Happy Calculating!!!

Regards,













Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
In order to find the equation of a line, you must know two things:
1) Slope
2) Y-intercept

In this problem, the slope must be found by writing the given equation in "slope-intercept" form. That is, you must solve for y in terms of x.
3x+5y=15
5y = -3x + 15

Divide both sides by 5:
%285y%29%2F5+=+%28-3x%29%2F5+%2B15%2F5
y+=+%28-3%2F5%29x%2B3

The slope of the given line is m=-3/5, so the slope of any line PARALLEL to this line is also m=-3/5.

Secondly, the given point (0,9) just happens to be the Y-intercept, so in the equation
y=mx+b
m=-3/5 and b=9
y=%28-3%2F5%29x%2B9+

R^2 at SCC