Select the correct answer.

Two points located on [tex]$\overleftarrow{ JK }$[/tex] are [tex]$J(1,-4)$[/tex] and [tex][tex]$K(-2,8)$[/tex][/tex]. What is the slope of [tex]$\overleftrightarrow{ JK }$[/tex]?

A. -4
B. -2
C. [tex]$-\frac{1}{4}$[/tex]
D. [tex][tex]$\frac{1}{4}$[/tex][/tex]
E. 4



Answer :

To find the slope of the line passing through points [tex]\( J(1, -4) \)[/tex] and [tex]\( K(-2, 8) \)[/tex], we can use the slope formula. The slope [tex]\( m \)[/tex] between two 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 coordinates:
- Point [tex]\( J \)[/tex]: [tex]\( (1, -4) \)[/tex]
- Point [tex]\( K \)[/tex]: [tex]\( (-2, 8) \)[/tex]

We can identify:
- [tex]\( x_1 = 1 \)[/tex]
- [tex]\( y_1 = -4 \)[/tex]
- [tex]\( x_2 = -2 \)[/tex]
- [tex]\( y_2 = 8 \)[/tex]

Substituting these values into the formula, we get:

[tex]\[ m = \frac{8 - (-4)}{-2 - 1} \][/tex]

Simplifying inside the numerator and denominator:

[tex]\[ m = \frac{8 + 4}{-2 - 1} \][/tex]
[tex]\[ m = \frac{12}{-3} \][/tex]
[tex]\[ m = -4 \][/tex]

Therefore, the slope of the line passing through points [tex]\( J \)[/tex] and [tex]\( K \)[/tex] is [tex]\(\boxed{-4}\)[/tex], which corresponds to answer choice A.