Final answer:
The equation that models the line through the point (12,3) with a slope of -⅓ is y = -⅓x + 7.
Step-by-step explanation:
The equation that models the line through the point (12,3) with a slope of -⅓ is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -⅓, so the equation becomes y = -⅓x + b. To find b, plug in the coordinates of the given point into the equation and solve for b.
Using the point (12,3), we have 3 = -⅓(12) + b. Simplifying further, we get 3 = -4 + b. Adding 4 to both sides, we find that b = 7.
Therefore, the equation of the line that goes through the point (12,3) with a slope of -⅓ is y = -⅓x + 7.