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.

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