## Objective:

**To use points to find the slope of the line.**

## Vocabulary:

**Slope**- The ratio of the vertical change to the horizontal change of a line.- It describes the
*rate of change*or slant of the line. - Think of it as "
*rise over run*".

- It describes the
**y**- Is read '_{2}*y sub 2*' and means '*y from the second point*'.**Grid Intersections**- Places where the grid lines intersect.

## Notes:

### Slopes:

When looking at the line going from left to right (like you read):- The slope is
*positive*if the line goes*up*. - The slope is
*negative*if the line goes*down*. - The slope is
*0 (zero)*if the line is*horizontal*. - The slope is
*undefined (no slope)*if the line is*vertical*.

*zero slope*and

*no slope*are

*NOT*the same thing!

- Zero slope has
*no rise*but*has run*. - No slope
*has rise*but*no run*.- No slope creates a fraction that has zero for the denominator.
- A ratio with zero for the denominator is
*undefined*.

### Slope Formula:

*y*is the y-value from the_{2}*second*point.*y*is the y-value from the_{1}*first*point.*x*is the x-value from the_{2}*second*point.*x*is the x-value from the_{1}*first*point.

### Hint:

An easy way to remember this is to think of skiing:- If the slope is a positive number then you are skiing uphill.
- If it is a negative number you are skiiing downhill.
- If the slope is zero you are skiing straight across.
- If the slope is undefined it is as if you skied off of a cliff ... and now (
*splat*) you are*UNDEFINED*!

## Examples:

- Locate two places where the line crosses grid intersections.

I see four in this graph: (−3, 6), (0, 4), (3, 2), & (6, 0).

Substitute the x and y values from two of these points into the slope formula and solve.

*Be careful with the signs*, this is where most mistakes are made.

It doesn't matter which two points you use. Using the last two points gives you the same answer.

- Locate two places where the line crosses grid intersections.

I see five in this graph: (−4, −3), (−3, −1), (−2, 1), (−1, 3) & (0,5).

Substitute the x and y values from two of these points into the slope formula and solve.

*Be careful with the signs*, this is where most mistakes are made.

It doesn't matter which two points you use. Using the last two points gives you the same answer.