Answer:
19) slope = undefined
20) slope = [tex]\mathsf{-\frac{5}{3} }[/tex]
Step-by-step explanation:
19) Graph of a vertical line
Given the graph of a vertical line, with coordinates of (-2, 3) and (-2, -3):
Since the formula for solving the slope of a line is given by:
[tex]\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}[/tex]
This implies that a vertical line has no horizontal change. Therefore, the value of the denominator in the given formula will be: x₂ - x₁ = 0. This division by zero is an undefined operation, hence the slope of a vertical line is undefined.
20) Find the slope of a line through the given pair of points.
Given the coordinates, (2, -9) and (-4, 1), substitute these values into the following slope formula:
[tex]\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}[/tex]
Let (x₁, y₁) = (2, -9)
(x₂, y₂) = (-4, 1)
Substitute these values into the given formula:
[tex]\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}[/tex]
[tex]\mathsf{m = \frac {1\: -\: (-9)}{-4\: -\:2}\:=\:\frac {1\: +\:9}{-6}\:=\:\frac{10}{-6}\:=\:-\frac{5}{3}}[/tex]
Therefore, the slope of the line is, [tex]\mathsf{m\:=\:-\frac{5}{3} }[/tex].
