SOLUTION: Directions ask: "Write an equation in slope-intercept form for each line according to the given information" Contains (3,5) Is parallel to 5x-2y=10

Question 28964: Directions ask: "Write an equation in slope-intercept form for each line according to the given information"
Contains (3,5)
Is parallel to 5x-2y=10
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
Directions ask: "Write an equation in slope-intercept form for each line according to the given information"
Contains (3,5)
Is parallel to 5x-2y=10

The given line is 5x-2y=10
The given point on the required line is P(3,%)
That is 5x-2y-10 = 0 ----(1)
Required to find the equation to a line
that is parallel to the given line and
that passes through the given point P(3,5)
Any line parallel to (1) will be of the form:
5x-2y+k = 0 ----(2)
[giving different values to k will give us different lines each parallel to the given line]
By data P(3,5) is a point on (2)
Therefore putting x=3 and y=5 in (2)
5X(3)-2X(5)+k=0
15-10 +k=0
5+k=0
k=-5
Putting k=-5 in (2) we get our required line
5x-2y-5=0 ----(*)
This is the equation to the required line in the general form.
But we are asked to present it in the slope and y-intercept form.
5x-5 =2y (keeping the yterm on one side and the other terms on the other side)
Dividing by 2,we get
(5/2)x+(-5/2) = y (making the coefficient of y equal to 1)
That is y = (5/2)x+(-5/2)
Which is in the slope and y-intercept form.
Here slope = (5/2) and y - intercept = (-5/2)
Answer: 5x-2y-5=0 or equivalently y = (5/2)x+(-5/2)
Verification: Checking for P(3,5)on this line
LHS =5x-2y-5 = 5X(3)-2X(5)-5=15-10-5 = 15-15 =0 =the RHS.
Therefore our equation is right
Note: Any line parallel to a given line Ax+By+C=0
is taken as Ax+By +D =0
What is the idea?
The idea is: lines parallel and so slopes equal.By taking the xterm and the yterm the same we are establishing that the slope = (-A/B) is the same for the parallel lines.
It is the different values that D takes that fetches different lines(A parallel beam)each parallel to the given line
Note: When the coefficient of y is 1 on one side,the coefficient of x on the other side is the slope of the line.

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