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...

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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**