<p>So for this question, what are you suppose to do? I just plugged in (squroot(3), 1) into every equation.</p>
<p>Is that the correct way to find the right answer? Also how do you convert degrees into slope??</p>
<p>It’s a question about special right triangles. If you drop a vertical line down from any point on that graph, you’ll create a 30-60-90 triangle with a short leg equal to the change in y, and the long leg equal to the change in x.</p>
<p>Since, in a 30-60-90 triangle the ratio of short leg to long leg is always 1/(√3), the slope of the line is 1/(√3). Your method was legit. :)</p>
<p>Drop a perpendicular line down to the x-axis. This gives you a right triangle which is a 30-60-90 triangle (because you have the 90 and 30 degree angles). Let the side on the x-axis be x. Because x is opposite the 60 degree angle, we know from the special triangles that the side-angle pairs are (30=y) ( 60= y\sqrt{3}) (90=2y) so x=y\sqrt{3} so y=(x\sqrt{3})/3. The side opposite the 30 degree angle is y = (x\sqrt{3})/3. This gives us the coordinates of the top point of the triangle, because we are given the x and y sides ( draw it out, you’ll see it), so the slope is y/x= (x\sqrt{3})/3 / x = \sqrt{3} / 3. That is the slope, so the equation is y= (x\sqrt{3})/3 or choice C (equivalent answer)</p>
<p>thanks guys!</p>
<p>One more thought…</p>
<p>You know that the line has equation y=mx where m is the slope. And they gave you the angle it makes with the x axis. Many students are totally surprised to find out that the slope of the line is the tangent of the angle. So y = tan(30) x is what you are looking for.</p>
<p>I’ve had students argue with me that tangent and slope have nothing to do with each other! After all, slope is rise over run but tangent is opposite over adjacent – those are two COMPLETELY different things… :)</p>
<p>pckeller, can you explain some more? I don’t quite get it! But your method sounds very interesting!</p>
<p>It’s something that’s true for any line: the slope of the line is equal to the tangent of the angle that the line makes with respect to the horizontal. (But 30, 45 and 60 degrees are the only ones that would ever be on the SAT.) If you don’t see why it’s true, draw a right triangle with a horizontal leg, a vertical leg and a hypotnuse that lies on the line in question. If I told you to find the tangent of the angle made with respect to the horizontal, you would divide the opposite by the adjacent. But the opposite is also called the rise. The adjacent is also called the run. So the tangent is also the slope. </p>
<p>I don’t know why, but it bothers me that this connection is rarely taught in school…not that it is so important, but to me it is a symptom of the compartmentalized way that math facts are often presented.</p>
<p>But BTW, your method was actually quite lazy and clever.</p>
<p>That method is very interesting. I think I’ll try it next time I see those kind of questions…</p>
<p>thank you (:</p>
<p>Not every mathematical connection can be taught in school- that would take too long. And this is something students should try to come up on their own, it’s not too difficult</p>
<p>Well, yes, you are right – you can’t teach 'em all. But there is a connectedness to math that I think gets overlooked. And math is more interesting when you do make the connections. For example, I’ll make it a puzzle: why is the ratio of the opposite over the adjacent called the “tangent”? When you first encounter that word in trig, it doesn’t seem connected to the way that word has been used in geometry…</p>
<p>This can also be solved if you are aware of the polar coordinate system. Look here:
<a href=“http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates.aspx[/url]”>http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates.aspx</a>
Two equations often used when converting things defined in the polar coordinate system to Cartesian: y = rsin(theta) and x = rcos(theta).
Average slope in the Cartesian coordinate system is defined as the change in y over change in x. The r here (distance from origin to the point) is the same for both equations, so it can be dropped. This leaves sin(theta) over cos(theta), or tan(theta). Once you find the slope (m) you can get an equation with y = mx + b.</p>
<p>LOL I’m learning that in precalc!</p>