Hello, Lydia,
You've asked a lot of questions in the past half hour. Please look over the responses for the problems that are similar. Please try answering a few on your own. This one is slightly different, so I'd like to help.
You are given two points. In theory, many equations could fit these two points: parabolas, for example. We'll assume here that a straight line is sought, which will have the format y = mx + b, where m is the slope and b is the y intercept.
The first thing to do is find the slope. This is the rate at which y changes as a function of x. If x goes up and y also goes up, it will have a positive slope, and vice versa. The size of m determines how quickly y changes. The slope can be calculated with the two given points using what is known as the "rise over the run" calculation. The "rise" is the change in the y value as given by the "run," or change in the x value.
In this case our two points are (6,7) and (-3,4). Let's reverse the order so that the lower x value is the first point: (-3,4) and (6,7). As we go from the first to the second point, x goes from -3 to 6. This is the run, and there is a distance of 9 between the two points (6 - (-3)=9.). The change in y value is the rise, and we find a change of 3 (7 -4 = 3). The slope is Rise/Run, or (3/9, or 1/3). This becomes the "m" in our equation:
y = (1/3)x + b
To find b, use one of the points in the equation and solve for b:
7 = (1/3)*6 + b
7 = 2 + b
b = 5
So our equation becomes y = (1/3)x + 5
Bob
