y=-1/3x-4;(-6,-3)

Question

need the equation of a line parallel to the given line but passing through the given point

Answer 1

Parallel means it has the same slope  -1/3

The -4 is where there line crosses the y axis.   The general form of a line is   y = mx + b  where m is the slope and b is where is crosses the y axis.

 

All you have so far is the slope = -1/3     so    y = -1/3 x + b 

But it must also go through ( -6, -3 )   where x = -6 and y = -3

Now substitute those values into  y = -1/3 x = b     and you get   -3 = -1/3 (-6) + b

Or     -3 = 2 + b

I will let you finish it to get the value of "b" and the line that is parallel and goes through ( -6, -3 )

 

I hope this helps.

 

Harvey M

Answer 2

So one of the forms of a linear equation is the slope-intercept form.

 

The equation given is in that form, so you should be able to pick off the slope, m, and the y-intercept, b.

 

What do you know about parallel lines and their slopes?

 

You're given a point, (x1,y1) = (-6,-3). So now use the point-slope form to get the equation you want:

y – y1 = m(x – x1)