Final answer:
The equation of the line with a slope of 1/2 that contains the point (6,-3) is y = (1/2)x - 6.
Step-by-step explanation:
The equation of a line can be determined using the slope-intercept form, which is y = mx + b where m is the slope and b is the y-intercept. Given that the slope (m) is 1/2 and the line contains the point (6, -3), we can substitute these values into the slope-intercept form to find the y-intercept b.
Starting with the slope-intercept form:
y = mx + b
Substitute the given point (x, y) = (6, -3) and slope m = 1/2:
-3 = (1/2)(6) + b
To find b, solve the equation:
-3 = 3 + b
b = -3 - 3
b = -6
Finally, we can write the equation of the line:
y = (1/2)x - 6