Final answer:
The equation of a line passing through the points (3, 6) and (8, 4) is calculated by first determining the slope, which is -2/5, and then using one of the points to find the y-intercept, resulting in y = -2/5x + 36/5.
Step-by-step explanation:
To find the equation of a line that passes through the points (3, 6) and (8, 4), we first need to calculate the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Plugging in our points, we get m = (4 - 6) / (8 - 3) = -2 / 5.
Next, we use the slope-intercept form of a line, which is y = mx + b, to find the y-intercept (b). We can use one of the points to solve for b. Let's use (3, 6):
6 = (-2/5)(3) + b
6 = -6/5 + b
6 + 6/5 = b
30/5 + 6/5 = b
36/5 = b
Now we have both the slope and the y-intercept, so the equation of the line is y = -2/5x + 36/5.