So, last episode I had mentioned a really great article which mentioned how it's currently possible to see 5 planets in the morning sky. Well, this weekend, I had a chance to check it out and managed to see Venus, Saturn, Mars, and Jupiter in the sky! Check out the pics below.
On to the line. In this episode we dig deep into the three major "anatomy points" of a line: the slope, y-intercept and x-intercept.
The slope: The "angle" of the line. From 0-45, the slope of the line is less than 1. From 45-90 we go from 1 to infinite slope. From 90-135 degrees, we go from the infinite back to -1, all negative. From 135 to 180, we go from -1 down to 0 again.
Next we introduce three critical linear equations. First the classic: y = mx + b, where m is the slope and b is the y-intercept. Example, y = 3x + 2, the slope is 3, and the line will intersect the y-axis at +2. Just think about what happens if you plug in x = 0, y = 3*0+2 = 2. Second we have the equation for slope: m = (y2-y1)/(x2-x1) using any two points on the line (x1,y1) and (x2,y2). We can then morph this into the "point-slope" form: y-y1 = m(x-x1) using any one point on the line.
Lastly, there are three combinations of two required pieces of information to define a line. Ideally, we would be given two points on a line, from this we could easily calculate m and then plug in for b. We could also be given a point and the y-intercept, and be able to make similar calculations. Lastly, we can be given one point and the slope, and do calculations to get everything we need.
