Assess Yourself

$(5, - 3)$ and $( - 5,\ 19)$
$( - 5,\ 19)$ and $( - 5,\ 3)$
$( - 3,\ 19)$ and $( - 5,\ 5)$
$(0,\ 0)$ and $( - 5,\ 5)$

Look at the $x$ -coordinates. If the ordered pairs were along the same vertical line, then these coordinates would be identical.

When a set of ordered pairs lies along the same vertical line, they have identical $x$ -coordinates.

Look at the $x$ -coordinates. If the ordered pairs were along the same vertical line, then these coordinates would be identical.

The coordinates of all the ordered pairs that lie along a horizontal line have identical $x$ -coordinates.
A horizontal line has a slope value of 0.
The graph of the line does not rise or fall as you read it from left to right.
It is a line that is perfectly flat.

When ordered pairs lie along the same horizontal line, they all have identical $y$ -coordinates.

All horizontal lines have a slope value of 0.

Horizontal lines do not rise or fall as you read them from left to right.

Horizontal lines are perfectly flat.

positive
negative
undefined
0

When the slope of a line is positive, the line increases as you read it from left to right.

When the slope of a line is negative, the line decreases as you read it from left to right.

The slope of every vertical line is undefined.

When a line is horizontal, its slope value is 0.

$m = - 1$
$m = \frac{6}{7}$
$m = 0$
The slope is undefined.

Be sure you correctly substitute the values into the slope formula, $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

When ordered pairs have identical $y$ -coordinates, then they lay along the same horizontal line. $( - 1, - 3)\left( 8, - 3 \right)$ ( $x_{1},\ y_{1})$ ( $x_{2},\ y_{2})$ $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{- 3 - ( - 3)}{8 - ( - 1)} = \frac{- 3 + 3}{8 + 1} = \frac{0}{9} = 0$

This is only true when the line is vertical.

$y$ -coordinate
Change in the rise
Origin
Slope

The $y$ -coordinate is the second number listed in an ordered pair.

The change in the rise of a line is the numerator of the slope formula.

The origin is the name for the ordered pair (0, 0)

The steepness of a line is its slope.

How well do you understand the concepts and skills introduced in this lesson?

Level Up

1. Which set of ordered pairs lies along the same vertical line?

2. Which is NOT true about a horizontal line?

3. Is the slope of Line A positive, negative, 0, or undefined?

4. Which is the slope value of the horizontal line that passes through the ordered pairs $( - 1, - 3)$ and $(8, - 3)$ ?

5. Which is another name for the steepness of a line?

Summary