Final answer:
The equation of a line with a slope of -2/3 that passes through the point (3, 1) is y = (-2/3)x + 3 by substituting the point into the slope-intercept formula and solving for the y-intercept.
Step-by-step explanation:
The question asks for the equation of a line with a slope of -2/3 that passes through the point (3, 1). The formula for the equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since the slope is given, we only need to solve for b by using the coordinates of the given point:
y = mx + b
1 = (-2/3)(3) + b
1 = -2 + b
b = 1 + 2
b = 3
Therefore, by substituting the slope and the calculated y-intercept into the equation, the equation of the line is:
y = (-2/3)x + 3