Answer:
The equation of the line is y = -3/7x - 23/7
Step-by-step explanation:
To start we need to find the slope of the original line. We can do this by solving the equation for y.
3x + 7y = 21
7y = -3x + 21
y = -3/7x + 3
Now we know the slope to be -3/7. Since parallel lines have same slopes, we know the new line also will have a -3/7 slope. We can now use that along with the given point in point-slope form to find the equation.
y - y1 = m(x - x1)
y + 5 = -3/7(x - 4)
y + 5 = -3/7x + 12/7
y = -3/7x - 23/7
