First, we need to get this equation out of its standard form outfit and into something a little more comfortable. If we change 2*x* – 4*y* = 12 into slope-intercept form, we'll have the slope right in front of us. We already know algebra, so changing this equation into *y* = ½*x* – 3 shouldn't be too big of a deal. Parallel lines have the same slope (which is ½ in this case), so our second line should have the equation *y* = ½*x* + *b*. The final piece of the puzzle is finding out what that *b* equals, and we can use the point (2, 2) to do that. *y* = ½*x* + *b* 2 = ½(2) + *b* 2 = 1 + *b*
*b* = 1
The equation of the line parallel to *y* = ½*x* – 3 that passes through (2, 2) is *y* = ½*x* + 1. Are we sure the lines are parallel? Both their slopes are ½, so yep. Are we sure the lines are different? Their equations are different, so yep. |