Question

Write an equation of the line satisfying the given conditions. Through (2, -5), parallel to 5x 6y + 7

Answer 1

We have to determine the equation of the line passing through the point (2,-5) and parallel to the line
`5x = 6y+7`

When two lines are parallel, then the slopes of the two lines are equal.

Equation of line with point
`(x_1, y_1)` and slope 'm' is given by:

`(y-y_1) = m(x-x_1)`

Since, we have to determine the equation of a line with point (2,-5).

So, the equation of the line is :
`(y-(-5)) = m(x-2)`

`y+5 = m(x-2)`

Since, the line is parallel to the line
`5x = 6y+ 7`

So,
`6y +7 = 5x`

`6y = 5x - 7`

`y = (5)/(6)x - (7)/(6)`

So, slope of the line 'm' is
`(5)/(6)`.

Therefore, the equation of the line is:

`(y+5) = (5)/(6)(x-2)`

`6y + 30 = 5x - 10`

`6y - 5x = -10-30`

`6y - 5x = -40`

Therefore,
`6y - 5x = -40` is the required equation of the line.