Algebraically determine the equation of a line in slope intercent form that is parallel to 5x-3y-8=0 and passes the x intercept of 4x-y+8=0

Question

Y=mx+b format

 

Answer 1

In slope-intercept form (y=mx+b), the line 5x-3y-8=0 is:

     y = (5/3)x - (8/3)

 

A parallel line has the same slope (that is, m), so the parallel line has the equation:

     y = (5/3)x + b

and we need a point to determine b.

 

The x-intercept of 4x-y+8=0 is the value of x when y=0.  So,

       4x-0+8 = 0

          4x = -8

            x = -2

   the x-intercept is (-2,0). Now, we can solve for b.

 

    0 = (5/3)(-2) + b

    0 = (-10/3) + b

    10/3 = b

 

The equation of the parallel line, in slope-intercept form, is:

    y = (5/3)x + 10/3