Solution - Properties of a line from two points

The slope of a vertical line is undefined

Equation of the line:

x = 16

x=16

x-intercept:

(16, 0)

(16,0)

The line is parallel to the to y-axis (no y-intercept)

See steps

Step-by-step explanation

1. Find the slope

The slope of a line between two points equals the change in the points' y-coordinates (rise) over the change in their x-coordinates (run).

The coordinates of point 1 are: $x_{1} = 16$ , $y_{1} = 19$
The coordinates of point 2 are: $x_{2} = 16$ , $y_{2} = - 9$

To find the slope, plug the points' x and y-coordinates into the formula and combine to simplify:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

$m = \frac{- 9 - 19}{16 - 16}$

$m = \frac{- 28}{0}$

Because dividing by zero is undefined, the slope is undefined

2. Find the line equation in slope intercept form

Because the line runs through two points with the same x-coordinate: $16$ , it is vertical.
Point 1 $(16, 19)$
Point 2 $(16, - 9)$

Because the line is vertical, all points on it have an x-coordinate of $16$ and its equation is:
$x = 16$

3. Find the x and y-intercepts

Because the line is vertical, every point on the line has an x-coordinate of 16

x-intercept: $(16, 0)$

The line is parallel to the to y-axis (no y-intercept)

4. Graph the line

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Why learn this

Whether they are horizontal, vertical, diagonal, parallel, perpendicular, intersecting, or tangent lines, it is a fact of life that straight lines are everywhere. Chances are, you know what a line is, but it is also important to understand their formal definition in order to better understand the various problems that involve them. A line is a one-dimensional figure, with a length but no width, that connects two points. After points, lines are the second smallest building blocks of shapes, which are essential for understanding our world and the spaces we find ourselves in. Additionally, understanding the slope, direction, and behavior of different types of lines is necessary for graphing and understanding certain types of information, an important skill across many industries.

Terms and topics

Properties of a straight lines