## Key Concepts

- Define slope of a line
- Find the slopes of lines in the coordinate planes
- Compare slopes of lines
- Identify parallel lines and perpendicular lines using their slopes

### Slope of a line

The ratio of vertical change (rise) to horizontal change (run) between any two points on the line is the slope of the line.

If a line in the coordinate plane passes through points (x_{1},y_{1}) and (x_{2},y_{2})

Then the slope of the line is

m=change in y /change in x

=y2−y1 / x2−x1

### Slopes of the lines in a coordinate plane

If a line rises from left to right, it is said to have a **positive slope.**

A horizontal line has **zero slope** (slope of 0).

When a line falls from left to right, it is said to have a **negative slope**

A vertical line has an **undefined slope**.

### Slopes of parallel lines

In a coordinate plane, two non-vertical lines are parallel if and only if they have the same slope.

### Slopes of perpendicular lines

In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is −1

.

## Exercise

- Line n passes through (0,2) and (6,5). Line m passes through (2,4) and (4,0). Is n⊥m? Explain.
- Line q passes through (0,0) and (-4,5). Line t passes through (0,0) and (-10,7). Which line is steeper, q or t?
- Find the slope of the line that passes through the points (-5,-1) and (3,-1).
- Graph the line through the given point with the given slope.
- P(-4,0) and slope 5/2
- Graph a line with the given description.
- Through (1,3) and perpendicular to the line through (-1,-1) and (2,0).

### Concept Map

### What we have learned

- The ratio of vertical change (rise) to horizontal change (run) between any two points on the line is the
**slope**of the line. - The slopes of parallel lines are equal.
- The product of slopes of perpendicular lines is -1.

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