# Scientific Notation (for fun and profit)

## What is the slope (m) of a line?

The slope of a line is the ratio of the change in y-coordinates to the change in x-coordinates of two points on the line. The change in y-coordinates is called the RISE and the the change in x-coordinates is called the RUN {to find the change in two numbers, subtract}. Sometimes we refer to the slope as the Rise/Run.

## What does the slope tell us?

The slope of a linear equation with two variable terms present tells us the direction of the graph (rising when positive, falling when negative).

## How can we use the slope?

When we know the slope of a line and a point on that line, we can easily graph the line by plotting the point and following the slope to another point on that line. So, the slope also gives us a set of directions from a point on a line to another point on that same line.

## How can we calculate the slope is we know two points on the line?

Since the slope is a ratio, it looks like a fraction. We are computing the difference in y-coordinates for the Rise and the difference in x-coordinates for the Run. So what will this look like?

m = y2 -y1 / x2 - x1,

where the coordinates of one point are (x1, y1) and the coordinates of the second point are (x2, y2).
Remember: since we are finding differences, you MUST keep the minus signs!

Okay, let’s do an example or three:

Ex. 1 Find the slope between (2, 4) and (7, 8).

m = y2 -y1 / x2 - x1,

Choose one of the points to use first. Let’s use (7, 8) this time.
{Remember: x2 and y2 are coordinates FROM THE SAME POINT!}

Begin by writing the pattern with the blanks for the coordinates (MUST keep minus signs!).

- / -   Now, fill in the coordinates from (7, 8), being careful to put the y-coordinate on top and the x-coordinate on bottom:

8-/7-  Next, we fill in the coordinates from (2, 4).

8-4 / 7-2  Calculate and simplify.

m = 4/5  Since the slope is positive, the line is Rising.

Ex. 2 Find the slope between (2, –4) and (–7, 8).

m = y2 -y1 / x2 - x1,

Choose one of the points to use first. Let’s use (–7, 8) this time.
{Remember: x2 and y2 are coordinates FROM THE SAME POINT!}

Begin by writing the pattern with the blanks for the coordinates (MUST keep minus signs!).

- / -   Now, fill in the coordinates from (7, 8), being careful to put the y-coordinate on top and the x-coordinate on bottom:

8-/-7-  Next, we fill in the coordinates from (2, 4-).

8-(-4) / -7-2  Calculate and simplify.

m = 12/-9 = 4/3  Since the slope is positive, the line is Falling.