Solve the problem.
-Find all points on the line through (-1, 7) and (15, -1) that lie between these two points and have integral coordinates.
A) (1, 7), (4, 5), (7, 3), (10, 1), and (13,0)
B) (1, 6), (3, 5), (5, 4), (7, 3), (9, 2), (11, 1), and (13, 0)
C) (0, 5), (1, 4), (2, 3) (3, 2), (4, 1), (5, 2), (6, 3), and (7, 4)
D) (3, 5), (7, 3), (11, 1) and (14, 0)

Question

Quizplus · Accepted Answer

First, find the slope of the line using the two given points: slope $m = \frac{-1 - 7}{15 - (-1)} = \frac{-8}{16} = -\frac{1}{2}$. The equation of the line can be found using point-slope form $y - y_1 = m(x - x_1)$, substituting one of the points and the slope: $y - 7 = -\frac{1}{2}(x + 1)$. Simplifying, we get $y = -\frac{1}{2}x + 7.5$. For integral coordinates between the two points, both $x$ and $y$ must be integers. By testing values of $x$ between -1 and 15, we find that the points (1, 6), (3, 5), (5, 4), (7, 3), (9, 2), (11, 1), and (13, 0) satisfy the line equation with integral coordinates.

Solve the Problem. -Find All Points on the Line Through (-1, 7) and (-1