Select the correct answer.

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



Answer :

To determine the slope of the line passing through two points, we can use the slope formula. The formula to find the slope [tex]\( m \)[/tex] of a line passing through points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:

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

Given the points [tex]\( J(-1, -9) \)[/tex] and [tex]\( K(5, 3) \)[/tex]:
- [tex]\((x_1, y_1)\)[/tex] corresponds to the coordinates of point [tex]\( J \)[/tex], which are [tex]\((-1, -9)\)[/tex].
- [tex]\((x_2, y_2)\)[/tex] corresponds to the coordinates of point [tex]\( K \)[/tex], which are [tex]\((5, 3)\)[/tex].

Now, plug these values into the slope formula:

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

Simplify the numerator and the denominator:

[tex]\[ m = \frac{3 + 9}{5 + 1} \][/tex]

Further simplification gives:

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

[tex]\[ m = 2 \][/tex]

Thus, the slope of the line [tex]\(\overleftrightarrow{ JK }\)[/tex] is [tex]\(\boxed{2}\)[/tex].

The correct answer is D.