Given a line with equation 3x +7y = 21. write an equation in point-slope form of the line parallel to the given line through the point (4, -5).

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

so far i think you have the right thing going for you just remember soh cah toh

step-by-step explanation:

sine over hypotenuse

cosine   equals adjacent

tangent over hypotenuse

i have not got your picture clearly so see it once again