Final answer:
To find the slope-intercept form equation of the line passing through the points (6, 1) and (3, 3), calculate the slope as -2/3 and use one of the points to find the y-intercept as 5. The equation of the line is y = -(2/3)x + 5.
Step-by-step explanation:
The question asks for the equation in slope-intercept form of the line passing through two given points. According to the formula, the slope (m) of a line passing through two points (x1, y1) and (x2, y2) is calculated as m = (y2 - y1) / (x2 - x1). Applying this to the points (6, 1) and (3, 3), we get:
m = (3 - 1) / (3 - 6) = 2 / (-3) = -2/3
The next step is to use one of the points and the slope to find the y-intercept (b) using the slope-intercept equation form y = mx + b. If we use the point (3, 3), we have:
3 = (-2/3)(3) + b
b = 3 + 2 = 5
Now we have both the slope and the y-intercept, so the equation is y = -(2/3)x + 5, making (b) the correct answer.