Algebra helpp? pleaseee! :(?

Question

Find a number, t, such that the line passing through the two given points has a slope of -2.

(t+1, 5);(6, -3t+7)

Answer 1

The slope of a line passing through the points (x1, y1) and (x2, y2) is given by:

slope = (y1 - y2) / (x1 - x2)

In your case the points are (t + 1, 5) and (6, -3t + 7).  Since you want the slope to equal -2, plug these values into the equation above and solve for t.

-2 = (y1 - y2) / (x1 - x2)

-2 = (5 - (-3t + 7)) / (t + 1 - 6)

-2 = (5 + 3t - 7) / (t + 1 - 6)   ...1 - 6 = -5

-2 = (5 + 3t - 7) / (t - 5)   ...5 - 7 = -2

-2 = (3t - 2) / (t - 5)   ...multiply both sides by (t - 5)

-2(t - 5) = 3t - 2   ...distribute the -2 on the left side

-2t + 10 = 3t - 2   ...add 2 to both sides

-2t + 10 + 2 = 3t - 2 + 2

-2t + 12 = 3t   ...add 2t to both sides

2t - 2t + 12 = 2t + 3t

12 = 5t   ...divide both sides by 5

12/5 = t

Hope this helps you!