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Distance, Slope, and Midpoint: Mastery Test

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


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. The slope formula for a line passing through 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 for points [tex]\( J \)[/tex] and [tex]\( K \)[/tex]:
- [tex]\( J(-1, -9) \)[/tex]
- [tex]\( K(5, 3) \)[/tex]

Let's denote:
- [tex]\( x_1 = -1 \)[/tex]
- [tex]\( y_1 = -9 \)[/tex]
- [tex]\( x_2 = 5 \)[/tex]
- [tex]\( y_2 = 3 \)[/tex]

Substitute these values into the slope formula:

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

Simplify the expression inside the numerator and the denominator:

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

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

Finally, divide the numerator by the denominator:

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

Therefore, the slope of [tex]\(\overleftrightarrow{ JK }\)[/tex] is:

[tex]\[ \boxed{2} \][/tex]

So, the correct answer is:
D. 2