if a line is parallel to another line, then the slopes must be the same. the easiest way to find the slope is to put your equation into slope-intercept form (or y=mx+c)so 2x + 2y = 3 put into slope-intercept form would bey = -x + (3/2) by getting y alone and dividing everything by 2.now we know that the slope is -1.
for our new line, we have y = -x + cif it passes through point (1,4) this means that we can solve for the c in the equation.to do this, we can plug in 1 for x and 4 for y and solve for cthen we would get4 = -1 + cc = 5
now we know that the equation for the new line is y = -x + 5