SOLUTION: I have a question on writing equations of parallel lines I understand that in order for an equation to be parallel with another, they must have the same slope. here is the proble

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Question 174012: I have a question on writing equations of parallel lines
I understand that in order for an equation to be parallel with another, they must have the same slope.
here is the problem
Write an equation of a line that passes through the point given and is parallel to the given line: (4,7), y= 5x-3
I do not know what to do. please explain the steps for further use.
Found 2 solutions by Mathtut, nerdybill:
Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
first you must write the equation in y=mx+b format or slope intercept form. the slope is m and the y intercept is b. Since the equation is already in that form we know what the slope is y=x-3. m=5. therefore as you say a line parallel to that line must have this same slope.
:
so we have the slope of 5. In order to write an equation of a line we need the slope and a point. We have both as (4,7) is the given point. Now we use the point slope formula which is y-k=m(x-h) where (h,k) is any point on the line
:
y-7=5(x-4)
:
y-7=5x-20
:
standard form point slope form

Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
The equation (of the line you want to be parallel with) was given as:
y= 5x-3
This is in the "slope-intercept" form:
y = mx + b
where
m is slope
b is the y-intercept
.
From the above, we now know the slope of:
y= 5x-3
is
m = 5
.
For two lines to be parallel, both of their slopes must be the same. Therefore, our "new" line mus have the slope of 5.
.
Given that we know the slope (5) and a single point (4,7) we stuff that into the "point slope" equation:
y - y1 = m(x - x1)
y - 7 = 5(x - 4)
Now, we manipulate to back into the "slope intercept" form:
y - 7 = 5x - 20
y = 5x - 13 (this is what they're looking for)