Question

Which of the following is the equation of a line parallel to the line y= -x + 1, passing through the point (4,1)

A.) x-y = -5 

B.) -x-y = 5

C.) x + y = -5

D.) x + y = 5

Answer 1

Slope - intercept form line equation is y = mx + b, where m is the slope and b is the y - intercept.

The line equation is y = - x +1.

Comapare the equation with slope - intercept form.

Slope (m) = - 1

Because the parallel lines have same slopes, the slope of the parallel line is - 1.

Now the parallel line equation is y = - x + b.

Find the y - intercept by substituting the point in the parallel line equation say (x, y) = (4,1).

1 = (- 1)(4) + b

b = 1 + 4

⇒ b = 5.

The parallel line equation is

y = -x + 5.

x+y =5

Option D is correct.