Find an equation of the line that satisfies the given conditions.?

Through (1, −1); parallel to the line x + 2y = 6

2y = -x + 6

y = (-1/2)x + 3

m = -1/2

point (1, -1)

y - y1 = m(x - x1)

y + 1 = -1/2(x - 1)

y + 1 = (-1/2)x + 1/2

y = (-1/2)x - 1/2 in slope-intercept form

- .--

x + 2y = 6 => y = 3 - x/2 => Slope = -1/2

Parallel lines have the same slope so the slope of the line passing through (1, -1) will also be -1/2:

y + 1 = -1/2*(x - 1)

y = -x/2 - 1/2

Obtain the slope from the given equation.

Which is m=-1/2

Now put in the general equation "(y-y1)= m (x-x1)

Where (x1,y1) is given in the ques..

Hope you got it now..