Final answer:
To find an equation for the line parallel to 3y - 24x = 18 and goes through the point (-3,8), we need to determine the slope of the given line and find the y-intercept using the given point. The equation of the parallel line is y = 8x + 32.
Step-by-step explanation:
To find an equation for the line parallel to 3y - 24x = 18 and passes through the point (-3,8), we need to determine the slope of the given line. The slope of a line can be found by rearranging the equation into the form y = mx + b, where m represents the slope. In this case, we need to isolate y and divide the coefficient of x.
3y - 24x = 18
3y = 24x + 18
y = 8x + 6
Since the parallel line has the same slope as the given line, the equation of the parallel line is y = 8x + b, where b is the y-intercept. To find b, we substitute the coordinates of the given point (-3,8) into the equation:
8 = 8(-3) + b
8 = -24 + b
b = 32
Therefore, the equation of the line parallel to 3y - 24x = 18 and goes through the point (-3,8) is y = 8x + 32.