# find the equation of a line passing through (1,-7) and parallel to 4x+9y=-1

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Two parallel lines have an equal slope. To find the equation of the line parallel to 4x+9y=-1 and passing through (1, -7) find the slope of 4x+9y=-1.

4x+9y=-1

=> `y = (-4/9)x - 1/9`

This is in the slope-intercept form and the slope is `-4/9`

The equation of a line passing through (1, -7) with a slope of `-4/9` is:

`(y + 7)/(x - 1) = -4/9`

=> 9y + 63 = -4x + 4

=> 4x + 9y + 59 = 0

**The equation of the required line is 4x + 9y + 59 = 0**

We have the line as 4x+9y=-1, let's convert this equation into y=mx+c form

4x+9y=-1

9y=-4x-1

y=-4/9x-1/9

So the slope is -4/9.

we know that parallel line have same slope.

So the parallel line passing through the point (1,-7)

Now, let put this (1,-7) in the equation with slope as -4/9, so that we can find the intercept.

y=mx+c

-7=(-4/9)*1+c

-7=-4/9+c

-7=(-4+9c)/9

-63=-4+9c

9c=-63+4

c=-59/9

so the equation of the line passing through the point (1,-7) and parallel to 4x+9y=-1is

y=(-4/9)x+(-59/9)

y=(-4x-59)/9

9y=-4x-59

**4x+9y+59=0**