I never got around to the following topics: Parallel lines have the same slope. A perpendicular line crosses at right angles and has a slope equal to the negative reciprocal of the slope of the other line.
Also scatter plots were not covered. Go back a few posts to Nov 22 to find Kahn Academy links to these and other topics.
Here's a solution to one of the harder problems:
Q. What is the y-intercept of the line which passes through (-3,-1) and (6,4)
A. There are many ways to solve this - here's one: Any equation for a straight line can be put in the form of y =
mx +
b.
We've got four letters in that equation. If we can figure out m, we can figure out b, because we have an (x,y) pair that makes the equation true. So let's figure out m, the slope.
STEP 1. Slope equals the rise (or change in the y co-ordinate) over the run (the change in the x co-ordinate).
the change in the y co-ordinate is -1 to 4, so it went up 5.
The change in the x co-ordinate is -3 to 6 or 9. So our slope (rise over run) is 5/9.
STEP 2. Now our equation is y = 5/9 x + b, but we know a couple of points which satisfy the equation. Let's use (6,4) so we don't have to deal with negative numbers. We'll substitute 6 for x and 4 for y:
STEP 3. 4 = 5/9 * 6 + b (Next we'll multiply 5/9 times 6)
4 = 30/9 + b (Let' reduce that fraction)
4 = 10/3 + b )Now subtract 10/3 or 3 1/3 from both sides)
2/3 = b (so b, the y-intercept = 2/3. What did the question ask? What is the y-intercept. Aha: 2/3 but we might want to express that as an ordered pair: (0, 2/3)
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