375. Give coordinates for a point that is 8 units from the line y = 5. Then find both pointson the line 3x + 2y = 4 that are 8 units from the line y = 5

Step 1: Find a point that is 8 units from the line y = 5

The line y = 5 is a horizontal line that crosses the y-axis at 5. A point that is 8 units from this line could be anywhere along the line y = 5 - 8 = -3 or y = 5 + 8 = 13. So, we can choose any x-coordinate we want. Let's choose x = 0 for simplicity. So, one such point is (0, -3) or (0, 13).

Step 2: Find points on the line 3x + 2y = 4 that are 8 units from the line y = 5

First, we need to find the points on the line 3x + 2y = 4 that lie on the lines y = -3 and y = 13.

For y = -3, substitute into the equation of the line:

3x + 2(-3) = 4 3x - 6 = 4 3x = 10 x = 10/3

So, one such point is (10/3, -3).

For y = 13, substitute into the equation of the line:

3x + 2(13) = 4 3x + 26 = 4 3x = -22 x = -22/3

So, the other point is (-22/3, 13).