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 174007: 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 3 solutions by nerdybill, Mathtut, gonzo:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website!
Write an equation of a line that passes through the point given and is parallel to the given line: (4,7), y= 5x-3
.
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)

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 gonzo(654)   (Show Source):
You can put this solution on YOUR website!
your new line general equation in slope intercept form is:
y = m*x + b
where:
m is the slope
b is the y intercept.
-----
the line you are parallel to is:
y = 5x-3
-----
this line is also in slope intercept form.
-----
the slope of the line you are parallel to is 5.
you need to make the slope of your new line = 5.
the equation for your new line is:
y = 5x + b
-----
since your new line passes through the point (4,7), then you need to use this information to complete the equation of your new line.
-----
there are two ways to do this:
-----
here is the first way:
-----
plug those values into the slope intercept form of the line.
that form is:
y = m*x + b
your slope is 5 making that equation:
y = 5*x + b
your point is (4,7).
you put 4 in for x and 7 in for y and solve for b.
7 = 5*4 + b
7 = 20 + b
subtract 20 from both sides:
b = 20-7 = -13
-----
the other way to solve this is:
-----
the general form of the equation for a line when you need to plug in a known point is:
(y-y1) = m*(x-x1)
this is also the slope intercept form of the equation, but that is not specified up front as you can see.
-----
you have:
m = 5
x1 = 4
y1 = 7
-----
that equation becomes:
(y-7) = 5*(x-4)
-----
you solve that equation by putting it into the slope intercept form.
you remove the parentheses:
y-7 = 5*x - 20
add 7 to both sides:
y = 5*x -20 + 7 = 5*x - 13
the equation of your new line should be:
y = 5*x - 13
this is the slope intercept form of the equation of a line.
the slope intercept form of the equation of a line is:
y = m*x + b
your equation:
y = 5*x - 13
makes:
m = 5
b = -13
-----
you got the same answer 2 ways which is good.
-----
to test if your answer is correct:
let x = 4 and solve for y.
y = 5*4 - 13
y = 20 - 13
y = 7
-----
the point (4,7) is on the line.
this is good.
equation looks good.
graph of:
y = 5x-3
and
y = 5x - 13
is shown below: