Final answer:
To find the equation of a line parallel to the given line, we need to find the slope of the given line first. The given line has the equation 3x + 6y = 30, which can be rewritten in slope-intercept form as y = (-1/2)x + 5. Since parallel lines have the same slope, the slope of the line parallel to the given line is also -1/2. Now, we can use the point-slope form of a linear equation to find the equation of the parallel line passing through (-8, 8).
Step-by-step explanation:
To find the equation of a line parallel to the given line, we need to find the slope of the given line first. The given line has the equation 3x + 6y = 30, which can be rewritten in slope-intercept form as y = (-1/2)x + 5. Since parallel lines have the same slope, the slope of the line parallel to the given line is also -1/2. Now, we can use the point-slope form of a linear equation to find the equation of the parallel line passing through (-8, 8).
Using the point-slope form, we have y - 8 = (-1/2)(x - (-8)). Simplifying this equation gives y - 8 = (-1/2)(x + 8), which can be further simplified to y - 8 = (-1/2)x - 4. Finally, we can rewrite this equation in slope-intercept form as y = (-1/2)x + 4.