Final answer:
The equation of the line parallel to y = 5 - ⅓x that goes through (-3,0) is y = -⅓x - 2.
Step-by-step explanation:
The student is asking for the equation of a line that is parallel to a given line and passes through a specific point. The given line is y = 5 - ⅓x, which means its slope is -⅓. Since parallel lines have the same slope, the line we are looking for will also have a slope of -⅓. Using the point-slope form, which is y - y₁ = m(x - x₁), where (x₁, y₁) is the point the line goes through and m is the slope, we can substitute the point (-3,0) and the slope -⅓ to find the equation of the parallel line:
y - 0 = -⅓(x - (-3))
y = -⅓x - 2