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:
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 ((x0,y0); in this case (4,1)), the equation of the line can be determined as y-y0=m(x-x0)
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:
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.