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