Find the equation of the line that passes through (2, -7) and is parallel to 5x+4y=7

Question

Find the equation of the line that passes through (2, -7) and is parallel to 5x+4y=7

Answer 1

equation of line:   y = m*x  +  b         where:  m = slope of line (rise/run)    and   b = y-intercept

 

                           

The line must pass through point (2,-7) or  x0 = 2 and y0 = -7

 

rearranging 5*x + 4*y = 7 equation in eqn of line form:  y = m*x + b

 

 4*y  =  -5*x  + 7

 

y = -(5/4)*x  + 7/4     therefore, slope = m = -5/4

 

For another line to be parallel to given line it must have the same slope, m = -5/4

 

Now use point that the line must pass through:

 

y - y0  = m*(x - x0)        where: x0 = 2   and y0 = -7

 

y - (-7)  = (-5/4)*(x - 2)

 

y  + 7 = (-5/4)*x + 5/2

 

y = (-5/4)*x + 5/2 - 14/2

 

y = (-5/4)*x - 9/2         Therefore, this line is parallel to the given line and passes through (2,-7)