 So to complete the topic of writing the equation of a line, let's consider what we really need. To write the equation of a line, we need two points, which is what we might expect from geometry, because two points define a unique straight line. But actually, the first thing that we do when we have those two points is to find the slope of the line, and so what we really need to write the equation of a line is one point and the slope. And as soon as we have that, we can write the equation of the line in point-slope form. And it's worth remembering that the point-slope form is the easiest way to write the equation of a line. So if I want to find the equation of the line through a given point with a given slope, we can immediately write down the equation in point-slope form. And if we're bored and need something else to do, if we have too much time on our hand, we can write this in slope-intercept form by doing a little bit of algebra. Since we can write the equation of a line given two points or a point and the slope, you'll always be given two points or a point and the slope. Ha! The universe isn't that kind, and neither am I. So we might be given a point and some condition on the slope. All we know what the point is. We just need the slope, but we don't have it. What we do know is the line is supposed to be parallel to another line, and that tells us something useful because we know something about the slopes of parallel lines. Parallel lines have the same slope. So all we have to do is figure out what the slope of this line is. So the thing to notice is that the equation of this line is given to you in slope-intercept form. And as the saying goes, if there's a gift course, use the mouse. Or something like that. Since the given equation is in slope-intercept form, we can read off the slope. The line has slope two-thirds. And so this means that we want a line with slope two-thirds that goes to the point one-four. So its equation will be... And since the problem doesn't specifically ask us to write the equation in slope-intercept form, we'll put off rewriting in that form until we have to. So here we have a bunch of points. The problem is only one of them is actually on our line. The other two tell us something about the slope, but not about the slope of the line that we're trying to write the equation for. But we do know that we want the line to be perpendicular to another line. So let's bring up what we know about the slopes of perpendicular lines. And that means we should find the slope of the line through the points one-five and three-negative-one. So we'll calculate that. The line perpendicular will have a slope that is the negative reciprocal. So that perpendicular slope will be... So I know the line will have slope one-third and goes to the point three-five. So its equation will be... And again we can leave it in this form until we have to do something with it.