The easiest way to find the line parallel to 3x -2y =5 through (1,2), we must set 3x - 2y = 5 into slope-intercept form
[tex]3x-2y =5\\-2y = -3x+5\\y = \frac{3}{2}x-\frac{5}{2}[/tex]
In slope-intercept form, y = mx + b, m is the slope. For two lines to be parallel, their slopes must be equal.
Thus the new line that is parallel to 3x - 2y = 5 must also have a slope of (3/2)x
[tex]y= \frac{3}{2} x+b[/tex]
To find b, we must plug in (1,2)
[tex]2 = \frac{3}{2}*1 + b\\b = \frac{1}{2}[/tex]
Thus the equation that is parallel to 3x-2y = 5 and passes through (1,2) is [tex]y = \frac{3}{2}x+\frac{1}{2}[/tex]
Hope that helps!
