- In the following figure, the lines have slopes of 3 and 5. The lines intersect at (10,15). How far is it between the x-intercepts of the lines?

The equation of the line with slope of 3 is $ y = 3x + b $ and with the point $ (10,15) $ is $ 15 = 3 (10) + b $ then the equation is $ y = 3x-15 $

Similarly, the slope is 5. Then the equation is $ y = 5x-35 $

The x interceptions are $ x = 5 $ for $ y = 3x-15 $ Y $ x = 7 $ for $ y = 5x-35 $. The distance between the two 2. Is this correct?

- In the following figure, the two lines are perpendicular, and intersect in $ (6.8) $. The intersections in and of the lines have a sum of zero. Find the area of the shaded region.

the equations of the lines are $ y = mx + b $ Y $ y = – ( frac {1} {m}) x-b $ since the intersections in and are opposite each other. If I reconnect the point, I have:

$ 8 = 6m + b $ Y $ 8 = – ( frac {1} {m}) (6) -b $

If I put these two equations together, I would have

$ 6m + b = – ( frac {1} {m}) (6) -b $

$ 6m = – frac {6} {m} $

$ 6m ^ 2 = -6 $

$ 6m ^ 2 + 6 = 0 $

$ 6 (m ^ 2 + 1) = 0 $

Here I am stuck because I have a negative root, so I'm pretty sure I tried this problem badly.