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

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

Sagot :

GinnyAnswer
To find the slope of the line passing through two given points, we use the slope formula. For the points \( J(1, -4) \) and \( K(-2, 8) \), the slope \( m \) is calculated as follows:

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Here, \( (x_1, y_1) = J(1, -4) \) and \( (x_2, y_2) = K(-2, 8) \). Substituting these values into the formula, we get:
[tex]\[ m = \frac{8 - (-4)}{-2 - 1} \][/tex]

First, compute the numerator:
[tex]\[ 8 - (-4) = 8 + 4 = 12 \][/tex]

Next, compute the denominator:
[tex]\[ -2 - 1 = -3 \][/tex]

Now, divide the numerator by the denominator:
[tex]\[ m = \frac{12}{-3} = -4 \][/tex]

Thus, the slope of the line passing through points \( J(1, -4) \) and \( K(-2, 8) \) is \( -4 \).

The correct answer is:
A. -4
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