A line passes through #(9 ,2 )# and #( 3, 5 )#. A second line passes through #( 4, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

If the second line is parallel to the first line, it will have the same slope as the first line. To find the slope of the first line, we use the formula:

$m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$

Using the points (9, 2) and (3, 5), we get:

$m = \frac{{5 - 2}}{{3 - 9}} = \frac{{3}}{{-6}} = -\frac{{1}}{{2}}$

So, the slope of the first line is -1/2. Since the second line is parallel to the first line, it will also have a slope of -1/2.

Now, using the point-slope form of a line equation:

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

We can use the point (4, 8) and the slope -1/2 to find the equation of the second line:

$y - 8 = -\frac{1}{2}(x - 4)$

Solving this equation for $y$, we get:

$y = -\frac{1}{2}x + 10$

Now, to find another point on this line, we can choose any value of $x$ and plug it into the equation to find the corresponding $y$ value. For example, if we choose $x = 0$, then:

$y = -\frac{1}{2}(0) + 10 = 10$

So, another point on the second line is (0, 10).