# The question in Your Turn Explanation(3 of 5)

• I cannot understand the explanation of the question in Your Turn Explanation(3 of 5)

• Basically, Prof. Loh just introduced the idea of slope, which is a measure of how "slanted" a line is. Qualitatively speaking, a line with a positive slope always goes upwards when you move from left to right, and a line with negative slope always goes downwards when you move from left to right (so it makes sense that a line with slope 0 is just horizontal-- it doesn't go up or down when you move from left to right).

Also, the further away from 0 a slope is, the "steeper" it is. (So, lines with slopes 5 or -7 would be "steeper" than a line with slope 2) This diagram might help:

The quantitative way of determining the slope of a line is to take two points on that line and calculate how much y increases and divide that by how much x increases between those two points. So for example, if the points are (1,2) and (5,3), then the line with those points has slope (3-2)/(5-1) = 1/4.

The main point of that specific video was to illustrate a cool fact about perpendicular lines: their slopes multiply to -1

In that particular problem, the slopes were 2 and -1/2. But Prof. Loh shows how this generalizes: given any line, you can draw a right triangles whose hypotenuse is on the line (1).

Then, to find a line perpendicular to the red one, you simply rotate the triangle. (2) The hypotenuse of the new triangle is a segment on the perpendicular line (if it isn't clear why, let me know!)

The above is basically what Prof. Loh did in Part 2 (with actual numbers, though). And then, to prove that in general, slopes of perpendicular lines multiply to -1, we assign variables to the legs of the purple triangle. (see 3)

The slope of the red line is (-a)/b. The slope of the blue line is b/a. (Using what we know about how to find slopes). And when you multiply the slopes: (-a)/b * b/a = -1, no matter what a and b are!

Hope that helped, and please let me know if you have further questions

• Thank you, but now, I am confused about the explanation of the following question in Your Turn Explanation(3 of 5)

• I mean I cannot understand where did those big numbers come from.