Hello, Gre,
Equations formatted in the style of y = mx + b are linear expressions that relate the values of x and y to each other. They are linear in the fact that they are always changing at the same rate, no matter what point you choose for x or y. m is defined as the slope of the equation. It says "for every unit change in x, y will change by a factor of m. The slope is also called "The Rise Over the Run." That can also read as "the change in the y value per change in the x value." A -5 for the slope means that every time you go up by 1 on the x axis, y will decrease by 5. That is why it is negative.
The second equation has a positive slope of 4. That means y will increase by 4 each time x increases by 1.
The "b" in the equation is what is known as the "y-intercept." It is the value of y when x = 0. (When x = 0, the point must lie somewhere on the y axis line that goes through the origin of the chart, (0,0). In the first equation, the y intercept is 1. The line for that equation will go through the point (0, 1). The second equation has a y intercept of -7. It will go through the point (0, -7).
I personally prefer the second equation since it has a positive slope and even at x = 0 there is still a 1 left. Think of it perhaps as your net worth over time. Keeps going up, and you were even born with a few bucks (1 in this case).
Lines with a negative slope annoy me. Is the equation measuring my humor index over time? Or is it predicting my popularity? And it has a negative y intercept. Not only am I losing popularity, I started with a dislike rating. :)
Bob
