 Suppose we want to graph the line through the point 5,4 with slope negative two-thirds. So we'll begin by plotting the point 5,4. Since we're given the slope, it's helpful to remember that slope is rise over run. And so this slope minus two-thirds, we can read this as minus two over three, or as two over minus three. Now because we like to read things from left to right, it's actually convenient if we always make the denominator positive. So let's read this slope as a rise over run of minus two over three. And what this means is that if we start at any point on the line and rise minus two, we go down to units, then run three units to the right, we'll get to another point of the line. And it's worth writing down that if we go down to and right three, we get to the point eight, two. And since this is a graph of a line, two points are enough to draw the line. Or let's try to draw the line through three-four perpendicular to the line y equals two-thirds x minus five. So we have a point three-four, so we'll graph it. Now the line we want is supposed to be perpendicular to another line. And so remember, the slope of a line perpendicular to a line with slope m will have slope minus one over m. So we do need to know what the slope of the line is, and remember that if our equation of the line is in the form y equals mx plus b, our slope is m, the coefficient of x. And so the line two-thirds x minus five has slope m equal to two-thirds. So the line perpendicular will have slope m equals minus one over two-thirds, which is equal to minus three-halves. And so we can read our slope as a rise over run of minus three over two. And so this means that if we start at any point on the line, we'll have out this one, and rise minus three, go down three units, then go right two units. We'll get to another point on the line. And again, it's worth noting that this would take us to the point five-one, and once we have two points on the line, we can draw the line. Or let's graph the line through one-negative-four parallel to the line y equals three-x plus seven. So we'll begin by plotting the point. Since we're talking about parallel lines, remember parallel lines have the same slope. So the line y equals three-x plus seven has slope m equal to three. And so a line parallel to y equals three-x plus seven will have slope m equal to three. And here it's useful to remember that for any number n, n itself is equal to n over one. And so our parallel line will have slope rise over run equal to three over one. And so if you start at any point on the line and rise three, go up three units, and then go right one unit, you'll get to another point on the line. And again, it's worth noting that this takes us to the point two-one, and since we have two points on the line, we can draw the straight line between the two points.