# A line segment is bisected by a line with the equation # 4 y + 9 x = 8 #. If one end of the line segment is at #(5 ,2 )#, where is the other end?

The other end is at

In slope-intercept form, write the following line:

The equation for the distance between the point and the line is provided by this reference. It is as follows:

Point is where the line's other end is located.

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First, find the slope of the given line by rearranging its equation into slope-intercept form (y = mx + b):

[ 4y + 9x = 8 ] [ 4y = -9x + 8 ] [ y = -\frac{9}{4}x + 2 ]

The slope of the line is ( m = -\frac{9}{4} ).

Since the given line bisects the line segment, the slope of the line segment is the negative reciprocal of ( -\frac{9}{4} ), which is ( \frac{4}{9} ).

Using the point-slope form of a line (y - y1 = m(x - x1)), where (x1, y1) is the given point (5, 2) and m is the slope ( \frac{4}{9} ):

[ y - 2 = \frac{4}{9}(x - 5) ]

Now, solve for y:

[ y = \frac{4}{9}x - \frac{20}{9} + 2 ] [ y = \frac{4}{9}x - \frac{20}{9} + \frac{18}{9} ] [ y = \frac{4}{9}x - \frac{2}{9} ]

So, the other end of the line segment is at the point ( \left( x, \frac{4}{9}x - \frac{2}{9} \right) ), where x can take any real value.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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