Final answer:
The equation of the line passing through the points (0, b) and (3, 1) is best represented by option b) y = (1/3)x + 1, as this fits the slope-intercept form y = mx + b with a slope of (1 - b)/3, simplified to 1/3 when b equals 1.
Step-by-step explanation:
To find the equation of the line passing through the points (0, b) and (3, 1), we need to use the slope formula and the point-slope form of a line. The slope (m) is calculated as the change in y over the change in x between two points. For the points (0, b) and (3, 1), the slope would be:
m = (1 - b) / (3 - 0) = (1 - b) / 3
Since one of the points is (0, b), which is where the line crosses the y-axis, b is also the y-intercept. Therefore, the equation of the line can be written in the slope-intercept form y = mx + b. Substituting our slope in, we have:
y = ((1 - b)/3)x + b
However, to match the provided answer choices, we need to express the slope in a simpler form. Since none of the choices have (1 - b) in the slope, but rather they have 1/3 or b, we can deduce that b must already be 1 in this case which simplifies our equation to:
y = (1/3)x + 1
Thus, the correct equation according to the provided answer choices would be option b) y = (1/3)x + 1.