Find an equation for the line that passes through the point (4, −8) and is parallel to the line 2x − 4y = 5.

Question

Find an equation for the line that passes through the point
(4, −8)
and
is parallel to the line
2x − 4y = 5.

Answer 1

The line 2x - 4y = 5 is in Standard Form, so let's write the desired line in Standard Form also.

 

The Standard Form of the equation al a line looks like Ax+By=C and the slope is (-A/B).  [Note: you may once and forever convert that to slope-intercept form (y=mx+b) and remember m].

 

The desired line has the same slope, so it has the formula 2x -4y = C  and we need the point (4,-8) to determine C.

                 2(4) - 4(-8) = C

                   8 + 32 = C

                      40 = C

 

The parallel line is:  2x - 4y = 40   or x - 2y = 20.   [same as:  y = (1/2)x - 10]

Answer 2

line is parallel to 2x − 4y = 5.

 

so first we will write this equation in slope intercept form so we can find slope

 

2x -4y =5

 

4y =2x -5

 

y =  (1/2)x -5/4

 

slope = m = 1/2

 

parallel line has same slope

 

so slope of line = 1/2

line goes through (4,-8)

 

y= mx +b

-8 =(1/2)4 +b

-8 =2+b

-10 =b

 

equation of line

y = mx + b

y=(1/2) x -10