Final answer:
The slope of the line that passes through the points (−2/3, 3/4) and (5/6, −1/2) is calculated using the rise over the run formula resulting in a slope of −5/8, which corresponds to answer choice D.
Step-by-step explanation:
To find the slope, m, of the line that passes through the points (−2/3, 3/4) and (5/6, −1/2), we use the formula for slope which is the rise over the run, or the change in y over the change in x. Essentially, the slope m is calculated by taking the difference between the y-coordinates and dividing by the difference between the x-coordinates of the points:
m = (y2 - y1) / (x2 - x1)
Substituting the given points, we get:
m = (−1/2 - 3/4) / (5/6 - (−2/3))
m = (−1/2 - 3/4) / (5/6 + 2/3)
m = (−2/4 - 3/4) / (10/6 + 4/6)
m = (−5/4) / (14/6)
m = (−5/4) × (6/14)
m = (−5/4) × (3/7)
m = −15/28
m = −5/8
So, the slope of the line is −5/8, which means the correct answer is D. −5/8.