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

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 slope formula:

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

Here, [tex]\((x_1, y_1)\)[/tex] represents the coordinates of point [tex]\( J \)[/tex] and [tex]\((x_2, y_2)\)[/tex] represents the coordinates of point [tex]\( K \)[/tex]. Substituting the given coordinates into the formula:

[tex]\[ \begin{aligned} x_1 &= -1, & y_1 &= -9, \\ x_2 &= 5, & y_2 &= 3 \end{aligned} \][/tex]

Using these values in the slope formula:

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

Simplify the expressions in the numerator and denominator:

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

This simplifies to:

[tex]\[ \text{slope} = \frac{12}{6} \][/tex]

Finally, divide the values:

[tex]\[ \text{slope} = 2.0 \][/tex]

Therefore, the slope of the line passing through points [tex]\( J \)[/tex] and [tex]\( K \)[/tex] is [tex]\( \boxed{2.0} \)[/tex].