Final answer:
The equation of a line parallel to -2x + 3y = 12 and going through the point (18,-4) is y = (2/3)x - 16, as it has the same slope of 2/3 but a different y-intercept, which is calculated using the given point.
Step-by-step explanation:
To find the equation of a line parallel to -2x + 3y = 12 and going through the point (18,-4), we need to first write the given equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
By rearranging the given equation, we get 3y = 2x + 12. Dividing by 3 gives us y = (2/3)x + 4. This is the slope-intercept form of the given equation, and it shows that the slope (m) of the line is 2/3.
Since parallel lines have the same slope, our new line will also have a slope of 2/3. To find the y-intercept (b), we can use the point that the line goes through, which is (18,-4). Using the slope-intercept form:
y = mx + b
-4 = (2/3)(18) + b
-4 = 12 + b
b = -16
Thus, the equation of the line parallel to -2x + 3y = 12 and going through the point (18,-4) is y = (2/3)x - 16.