Explanation
Algebra / Graphs and Functions / Graphing Slope / Slope of a Line Using Two Points
In this problem, we have a set of the coordinates of two pairs of points, and we must compute the slope for each one of the sets.
For the line that passes through points (x₁, y₁) and (x₂, y₂), the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}.[/tex]
(11) (x₁, y₁) = (5, -2) and (x₂, y₂) = (6, -5)
Replacing the coordinates of these points in the formula above, we get:
[tex]m=\frac{-5-(-2)}{6-5}=\frac{-5+2}{1}=-3.[/tex]
(12) (x₁, y₁) = (3, 8) and (x₂, y₂) = (-4, 8)
Replacing the coordinates of these points in the formula above, we get:
[tex]m=\frac{8-8}{-4-3}=\frac{0}{-7}=0.[/tex]
A slope equal to zero represents an horizontal line.
(13) (x₁, y₁) = (7, 2) and (x₂, y₂) = (7, 4)
Replacing the coordinates of these points in the formula above, we get:
[tex]m=\frac{4-2}{7-7}=\frac{2}{0}=\infty.[/tex]
A slope equal to infinity represents a vertical line.
Answer
11. m = -3
12. m = 0 (horizontal line)
13. m = ∞ (vertical line)
