Write an equation of the line satisfying the given conditions.

through (1,−5); parallel to 5x=6y+7

ANSWER:

The line equation of required line is 5x – 6y – 35 = 0.

SOLUTION:

Given, line equation is 5x = 6y + 7 and the point is p (1, -5).

We have to find the line equation of a line that is parallel to given line and passing through point p.

First, let us find slope of given line.

5x = 6y + 7

5x – 6y – 7 = 0

We know that, parallel lines will have same slope, so slope of required line is

Now, we have slope and a point through it.

So, let us find the point slope form of the line i.e

Line equation →

6y + 30 = 5x – 5

5x – 6y – 5 – 30 = 0

5x – 6y – 35 = 0

Hence, the line equation of required line is 5x – 6y – 35 = 0.

Solve equation [2] for the variable y

[2] y = 8x + 7

// Plug this in for variable y in equation [1]

[1] 4x - 5•(8x+7) = -9

[1] -36x = 26

// Solve equation [1] for the variable x

[1] 36x = - 26

[1] x = - 13/18

// By now we know this much :

x = -13/18

y = 8x+7

// Use the x value to solve for y

y = 8(-13/18)+7 = 11/9

Solution :

{x,y} = {-13/18,11/9}