SOLUTION: I need help with this problem. It is an writing assignment. Write an equation of the line passing through (5,0) and parallel to the line y= 5x-2. Thanking you in advance

Algebra ->  Linear-equations -> SOLUTION: I need help with this problem. It is an writing assignment. Write an equation of the line passing through (5,0) and parallel to the line y= 5x-2. Thanking you in advance      Log On


   

Question 111907: I need help with this problem. It is an writing assignment.
Write an equation of the line passing through (5,0) and parallel to the line y= 5x-2.
Thanking you in advance
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The first thing to realize is that lines are parallel if and only if their slopes are equal. Conveniently, the given line is already in slope-intercept form y=mx%2Bb, so we can tell directly that the slope of the desired line is 5.

Knowing the slope of a line and a point that is not a y-intercept, we can use the point-slope form of a line to derive the desired equation:

%28y-y%5B1%5D%29=m%28x-x%5B1%5D%29

Now all we have to do is plug in the x and y values from the given point to obtain:

y-0=5%28x-5%29, and then simplify:

y=5x-25

Note that the answer checks because the derived line and the given line have equal slopes, therefore they are parallel, and if you substitute 5 (the x-coordinate of the given point) into the derived equation, you get y=0, (the y-coordinate of the given point).