Geometry Question

Question

The equation of line CD is y=-2x-2. Write an equation of a line parallel to line CD in slope-intercept form that contains point (4,5)

Answer 1

The equation of line CD is y=-2x-2. Write an equation of a line parallel to line CD in slope-intercept form that contains point (4,5)

 

The slope intercept form of a straight line is y = mx+b where m is the slope and b is the y-intercept.  For line CD, m = -2 and b = -2.  Any line parallel to CD will have the same slope, m = -2, but a different y-intercept, b.  So its equation would be:

 

y = -2x + b

 

To find b, plug in the point (4,5) from the problem statement:

 

5 = (-2)(4) + b

5 =  -8 + b

13 = b

 

So the equation of the line parallel to CD that passes through the point (4,5) is:

 

y = -2x + 13