# 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

**-coordinates is called the RISE and the the change in**

*y***-coordinates is called the RUN {to find the change in two numbers, subtract}. Sometimes we refer to the slope as the Rise/Run.**

*x*## 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

**-coordinates for the Run. So what will this look like?**

*x*m = y_{2} -y_{1} / x_{2} - x_{1},

where the coordinates of one point are (x_{1}, y_{1}) and the coordinates of the second point are (x_{2}, y_{2}).

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 = y_{2} -y_{1} / x_{2} - x_{1},

Choose one of the points to use first. Let’s use (7, 8) this time.

{Remember: x_{2} and y_{2} 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

**-coordinate on bottom:**

*x*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 = y_{2} -y_{1} / x_{2} - x_{1},

Choose one of the points to use first. Let’s use (–7, 8) this time.

{Remember: x_{2} and y_{2} 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

**-coordinate on bottom:**

*x*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.