Given that the line is parallel to y = -4 is the first clue. The line y = -4 is a horizontal line. All horizontal lines have a zero slope.Since your equation is parallel to that it must have the exact same slope. So you will use m = 0.Then plug in the (3,3) for the x and y in the slope intercept form of an equation and solve for b.y = mx +b3 =0 (3) + b3 = 0 + b3 = bSo to write the equation required for this question substitute the 3 in for the b and the zero in for the m (slope) and simplify.y = mx + by = 0x + 3y = 3 The answers from Katherine and Michael were the best method for solving. This is just another way to do the problem if you are not familiar with point slope form. 7/20/2013 | Bethanie F. CommentKatherine P.Saint Paul, MN0 0This problem provides you with a point (3,3) and a slope (parallel to y = -4, which is a slope of zero).Let's save you some time by using point slope form to write your equation.y - y1 = m(x - x1)y - 3 = 0(x - 3)y - 3 = 0y = 3 <-- the equation for your line :)7/18/2013 | Katherine P. CommentMichael W.Roseville, CA0 0Having the line parallel to y=-4 tells you the slope (parallel lines have the same slope). Since there is no coefficient to the "x" value (ie a slope of zero : y= 0x - 4), the slope of your new line is also 0 (m=0).Now for the y intercept value: plug your m (slope) into the standard slope intercept formula y=mx+b and include your point that the new line passes through. You then get the following:3=0(3) +b0 times 3 is 0, so your equation becomes 3=bYour equation is y=mx +b : mx=0, so it becomes y=b or in this case y=3 7/18/2013 | Michael W. CommentClaribel C.Schertz, TX0 4A parallel line will have the same slope as y=-4. To better understand line y=-4 you must write it as the line equation (y=mx+b). In order to have y=-4, the slope (m) must be -4, x must equals 1 and the intercept (b) must be 0. The line equation the would be y=-4x+0. Now that you have the line equation, let's find the parallel line that passes through (3,3). To find the parallel line equation you must substitute values y and x by (3,3) in the first line equation and determine the corresponding intercept.3=-4*3+b3=-12+b3+12=b15=bTherefore, the line equation for the line that passes through (3,3) and is parallel to y=-4 is:y=-4x+157/18/2013 | Claribel C. CommentCommentsNot meaning to disagree, but the line y=-4 is a horizontal line and therefore has a slope of zero (there is no "rise"), so the "m" must be zero. Any value of x would give you a y value of -4.Therefore the correct equation of the given line is y=0x - 4. A parallel line running through (3,3) would have the formula y=3.Your line would intersect y=-4 at (19/4, -4) or (4.75, -4).7/18/2013 | Michael W.
