To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the values of the slope (m) and the y-intercept (b).
First, let's find the slope (m) using the coordinates (5,6) and (8,4):
m = (y2 - y1) / (x2 - x1)
= (4 - 6) / (8 - 5)
= -2 / 3
Now that we have the slope, we can use one of the given points, for example (5,6), to find the y-intercept (b). Substituting the values into the slope-intercept form equation:
y = mx + b
6 = (-2/3)(5) + b
Solving for b:
6 = -10/3 + b
b = 6 + 10/3
b = 18/3 + 10/3
b = 28/3
Therefore, the equation of the line passing through (5,6) and (8,4) in slope-intercept form is:
y = (-2/3)x + 28/3