Question

6
y
LO
5
4-
-6 -5 -4 -3 -2 -1
-3
3-
2
1-
-0-
0
1
2
-1
-2-
-3-
-47
-5-
-6-
4 5
6
x
going from 5,6 -6, -1

Answer 1

Do you want the equation/slope, midpoint, distance, or a set of points to draw the segment from (5, 6) to (−6, −1)? I can also plot it on the grid you showed if you want — tell me which.

Meanwhile, here are the common useful results for the segment from (5,6) to (−6,−1):

- Slope: m = (−1 − 6)/(−6 − 5) = −7/−11 = 7/11.
- Equation (point–slope): y − 6 = (7/11)(x − 5). In slope–intercept form: y = (7/11)x + 31/11 (≈ (7/11)x + 2.81818).
- Midpoint: ((5 + (−6))/2, (6 + (−1))/2) = (−0.5, 2.5).
- Distance (length): sqrt(11^2 + 7^2) = sqrt(170) ≈ 13.0384.
- x-intercept: x = −31/7 ≈ −4.4286. y-intercept: 31/11 ≈ 2.8182.
- Integer lattice points on the infinite line: (x,y) = (5 + 11t, 6 + 7t) for any integer t. (For t=0 gives (5,6); t=−1 gives (−6,−1).)

If you want, I can give the y-values for each integer x from −6 to 5 (for plotting).