Final answer:
The equation of the line passing through (6,8) and (10,2) is found using slope formula and point-slope form. The slope is -3/2 and the equation is y = -3/2x + 17.
Step-by-step explanation:
To find the equation of the line that passes through the points (6,8) and (10,2), we need to calculate the slope and use one of the points to solve for the y-intercept. The slope (m) is calculated as the change in y divided by the change in x between two points, so:
m = (y2 - y1) / (x2 - x1)
m = (2 - 8) / (10 - 6) = -6/4 = -3/2
With the slope and one of the points, we can use the point-slope form to derive the equation of the line:
y - y1 = m(x - x1)
With point (6,8), the equation becomes:
y - 8 = (-3/2)(x - 6)
y = (-3/2)x + 9 + 8
y = (-3/2)x + 17
Thus, the correct equation for the line is option B: y = -3/2x + 17.