A line parallel to x + 4y = 4 and goes through the point (4, 1).

Answer 1

If you are asking to find the line parallel to x + 4y = 4.

Then, start by putting x + 4y = 4 in Slope Intercept Form by solving for y

y = mx + b

x + 4y = 4

Subtract y for both sides of the equation

x + 4y - 4y = -4y + 4

x = -4y + 4

Subtract 4 from both sides of the equation

x - 4 = -4y

Divide both sides of the equation by negative 4

-x/4 + 1 = y

So in the Slope Intercept form we have

y = (-1/4)x + 1

With slope m = -1/4

A line parallel to this would have the same slope of negative 1/4 and we can use the coordinates (4,1) to solve for b

1 = (-1/4)4 + b

1 = -1 + b

Add 1 to both sides of the equation

1 + 1 = b

2 = b

y = -1/4x + 2

You can graph your lines at Desmos.com to confirm that they are parallel.