SOLUTION: I need to write an equation in point intercept form for the line that is parallel to the given line and that passes through the given point for 4y=x (4,0) I got y=1/4x-0. is that c

Algebra ->  Linear-equations -> SOLUTION: I need to write an equation in point intercept form for the line that is parallel to the given line and that passes through the given point for 4y=x (4,0) I got y=1/4x-0. is that c      Log On


   

Question 680824: I need to write an equation in point intercept form for the line that is parallel to the given line and that passes through the given point for 4y=x (4,0) I got y=1/4x-0. is that correct?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
line 4y=x that passes through (4,0)
you got y=%281%2F4%29x-0 which is slope-intercept form where slope m=1%2F4 and y-intercept is 0
now find an equation in point-intercept form for the line that is parallel to the given line and that passes through the given point

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is 1%2F4 (its from the slope of y=%281%2F4%29%2Ax%2B0 which is also 1%2F4). Also since the unknown line goes through (4,0), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-0=%281%2F4%29%2A%28x-4%29 Plug in m=1%2F4, x%5B1%5D=4, and y%5B1%5D=0



y-0=%281%2F4%29%2Ax-%281%2F4%29%284%29 Distribute 1%2F4



y-0=%281%2F4%29%2Ax-4%2F4 Multiply



y=%281%2F4%29%2Ax-4%2F4%2B0Add 0 to both sides to isolate y

y=%281%2F4%29%2Ax-4%2F4%2B0%2F4 Make into equivalent fractions with equal denominators



y=%281%2F4%29%2Ax-4%2F4 Combine the fractions



y=%281%2F4%29%2Ax-1 Reduce any fractions

So the equation of the line that is parallel to y=%281%2F4%29%2Ax%2B0 and goes through (4,0) is y=%281%2F4%29%2Ax-1


So here are the graphs of the equations y=%281%2F4%29%2Ax%2B0 and y=%281%2F4%29%2Ax-1



graph of the given equation y=%281%2F4%29%2Ax%2B0 (red) and graph of the line y=%281%2F4%29%2Ax-1(green) that is parallel to the given graph and goes through (4,0)