Write the standard form of the equation of the line that passes through the point (4,1) and is parallel to the line 3x + 2y = 5.

## Write the standard form of the equation of the line that passes through the point (4,1)and is parallel to the line 3x + 2y = 5.

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# 3 Answers

The desired equation can be worked out using the following general formula:

y - y1 = m( x -x1) where m is the slope and (x1,y1) is the one point we know - here (4,1)

To get the slope we rearrange the given line as y = -(3/2) x + 5/2 Once in this form we

see that the slope is -(3/2). Since we want a parallel line the slope m also equals -(3/2)

Putting this together we ge

y - 1 = -(3/2) ( x - 4)

This can be rearranged into the slope intercept form.

y = -(3/2) x + 7

Paige:

The first step is to determine the

**slope**of the equation we're trying to solve for. Since two parallel lines have**the same slope,**we need to compute the slope (m) of the equation**3x+2y=5.**This can be obtained by converting the equation into**slope-intercept form**(i.e., y=mx+b, where m is the slope):So, let's first isolate the y term on the left side, by subtracting 3x from both sides, and then simplifying:

**3x+2y-3x=5-3x**

**2y =-3x+5**

Then, let's divide both sides by 2, to obtain slope-intercept form:

**y = (-3/2)x+(5/2)**

**From this, we know that the slope (m) is -3/2**

The next step is to determine the equation of the line we're being asked to solve for. If we know the slope (in this case m=-3/2) along with any given point on the line ((x

_{0},y_{0})_{; }in this case (4,1)), the equation of the line can be determined as**y-y**_{0}=m(x-x_{0})So substituting, the equation of the line is

**y-1=(-3/2)(x-4)**We now need to put this into standard form, with both x and y terms on the left side of the equation:

First, distribute the 3/2 on the right side:

**y-1=(-3/2)x+(3/2)4 or y-1=(-3/2)x+6**Next, add (3/2)x to both sides, add 1 to both sides, and simplify:

**(3/2)x+y=7**Finally, we can multiply both sides by 2, to eliminate the fraction (3/2):

**3x+2y=14****(This is the equation of the new line in standard form)**.Hope this helps.

George T.

You will use the equation : Y-Y

_{1}=m(x-x_{1}) where m is your slope.Since the lines are parallel they will have the same slope, so first you must solve for the slope, by making the first equation standardized.

3x+2y=5

2y=5-3x

y=(5/2)-(3/2)x

The slope is -(3/2)

Now to get the equation of the line using the points (4,1) use the first equation.

Y-1=-(3/2)(x-4)

Y-1=(-3/2)x+6

Y=(-3/2)x+7

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