**Problem:** Identify the slope, y-intercept, and x-intercept of the line 8x + 2y = 13.
**Solution** (with communication):
8x + 2y = 13 ==> 2y = -8x + 13
==> y = -4x + 6.5.
The slope of the line is -4.
x = 0 ==> y = 6.5 (the y-intercept).
y = 0 ==> 8x = 13 ==> x = 13/8 (the x-intercept). |
**Problem: **Two positive single-digit integers have a sum of 15. Find the integers.
**Solution** (with communication):
If the desired integers are represented by x and y, then x + y = 15 ==> y = -x + 15. This line contains all pairs of numbers that add up to 15. However, we only want pairs (x,y) that are positive single-digit integers. The only possibilities are (6,9), (7,8), (8,7), and (9,6). These are points on the line y = -x + 15.
Responding to the question as asked, there are two integer sets that meet the specified conditions. They are {6,9} and {7,8}.
Note: Watch your notation here. Don't confuse number sets (use of brackets) with points represented as ordered pairs (use of parentheses). |