kitchen table math, the sequel: true confession

## Saturday, December 29, 2007

### true confession

I found the wild-goose-chase problem, the one that took me many steps not to do while C. solved it at once using "logic and reasoning."

Find the value of r so the line that passes through each pair of points has the given slope.

44. (-2, 7), (r, 3), m = 4/3 *

C.'s solution:
7 - 3 = 4/3 (-2 - r)
4 = (-8 - 4r)/3
12 = -8 - 4r
20 = -4r
r = -
5

My non-solution:
y = 4/3x + b
7 = 4/3(-2) + b
7 = -8/3 + b
21/3 + 8/3 = b
29/3 = b

I seem simply to have stopped at this point. I don't know why. Looking at my solution page now is a bit like examining a single-vehicle accident scene trying to determine how the driver flipped his car twice in broad daylight & nice weather.

Alternatively, I didn't stop with 29/3 = b (I remember having done more steps) but the rest of my perambulations are recorded on some other piece of paper, not this one.

We'll never know.

* source: Glencoe Algebra, p. 261

LynnG said...

It has been a long time since I did geometry (other than watch my son survive it); but it looks like you correctly solved for the y-intercept.

Unfortunately, you weren't trying to find the y-intercept, so it was the wrong procedure, otherwise the math is good (for finding the intercept).

This is a great example of the Wild Mathematical Goose. You had a procedure that looked to be somewhat relevant, i.e., it involved slope and x,y coordinates, but answered the wrong question.

Apparently, you need more spaced repetition.

LynnG said...

Alternatively, you can arrive at C's answer by plotting the known point on graph paper, draw a line through (-2,7) with a slope of 4/3 and look where it intersects a horizontal line at y=3. The intersection point is your missing x coordinate.

Catherine Johnson said...

I love stuff like this because our kids are CONSTANTLY being hammered for irresponsibility, etc....and here I am, teaching myself math, highly motivated, and I'm failing to read the problem and follow directions.

Of course, this is why I'm committing 2008 to Behavior Management.

(Still want to do that book club - haven't figured out how....)

David said...

Although it's not the most direct solution, this is a very good start. You have found that the equation of the line is y = (4/3)x + 29/3. Substituting (r,3) into the equation of the line yields 3 = (4/3)r + 29/3, which you can solve for r.

Catherine Johnson said...

Hi David!

Yes, I think I probably just forgot what the problem asked for and found the y-intercept on autopilot.

I do wonder, though, whether I would have seen the more direct solution if I'd read the problem more closely.

I tend to think not.

ALTHOUGH, to be perfectly accurate, I remember doing these homework sets in a state of exhaustion and frayed nerves (book deadline)....so I think I do better when I'm more focused on math.

Even so, wild goose chases happen to me pretty regularly.