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Two points located on [tex]\overleftrightarrow{JK}[/tex] are [tex]J(-1, -9)[/tex] and [tex]K(5, 3)[/tex]. What is the slope of [tex]\overleftrightarrow{JK}[/tex]?

A. -2
B. [tex]-\frac{1}{2}[/tex]
C. [tex]\frac{1}{2}[/tex]
D. 2

Sagot :

To determine the slope of the line passing through the points [tex]\( J(-1, -9) \)[/tex] and [tex]\( K(5, 3) \)[/tex], we can use the formula for the slope of a line given two points:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of point [tex]\( J \)[/tex], and [tex]\((x_2, y_2)\)[/tex] are the coordinates of point [tex]\( K \)[/tex].

1. Identify the coordinates of the points [tex]\( J \)[/tex] and [tex]\( K \)[/tex]:
- [tex]\( J(x_1, y_1) = (-1, -9) \)[/tex]
- [tex]\( K(x_2, y_2) = (5, 3) \)[/tex]

2. Substitute these values into the slope formula:

[tex]\[ m = \frac{3 - (-9)}{5 - (-1)} \][/tex]

3. Simplify the numerator and the denominator:
- The numerator [tex]\( y_2 - y_1 = 3 - (-9) = 3 + 9 = 12 \)[/tex]
- The denominator [tex]\( x_2 - x_1 = 5 - (-1) = 5 + 1 = 6 \)[/tex]

4. Calculate the slope:

[tex]\[ m = \frac{12}{6} = 2 \][/tex]

Therefore, the slope of the line passing through the points [tex]\( J \)[/tex] and [tex]\( K \)[/tex] is [tex]\( 2 \)[/tex].

The correct answer is:
D. 2