Final answer:
The equation of the line passing through the point (3, -2) with a slope of 1/3 is y + 2 = (1/3)(x - 3), which simplifies to y = (1/3)x - 1.
Step-by-step explanation:
To write an equation of a line that passes through a specific point and has a given slope, we can use the point-slope form of a line's equation, which is expressed as:
y - y1 = m(x - x1),
where (x1, y1) is the point the line passes through and m is the slope. For the point (3, -2) with a slope of 1/3, the equation becomes:
y + 2 = (1/3)(x - 3).
We can also convert this to the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Distributing the slope on the right side and moving terms around, we get:
y = (1/3)x - 1.
The y-intercept (b) of this line is -1, and as expected, the slope is 1/3, indicating a rise of 1 on the vertical axis for every increase of 3 on the horizontal axis.