Line $AB$ contains points $A(3,-2)$ and $B(1,8)$. The slope of line $AB$ is
A. 5
B. -5
C. $\frac{-1}{5}$
D. $\frac{1}{5}$
Answer (2)
Identify the coordinates of points A and B on the line.
Apply the slope formula: m = x 2 − x 1 y 2 − y 1 .
Substitute the coordinates into the formula: m = 1 − 3 8 − ( − 2 ) .
Calculate the slope: m = − 5 .
Explanation
Problem Analysis We are given two points on line A B : A ( 3 , − 2 ) and B ( 1 , 8 ) . Our goal is to find the slope of this line.
Slope Formula The slope of a line passing through two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by the formula: m = x 2 − x 1 y 2 − y 1 In our case, ( x 1 , y 1 ) = ( 3 , − 2 ) and ( x 2 , y 2 ) = ( 1 , 8 ) .
Calculation Substitute the coordinates of points A and B into the slope formula: m = 1 − 3 8 − ( − 2 ) = 1 − 3 8 + 2 = − 2 10 = − 5
Final Answer Therefore, the slope of line A B is − 5 .
Examples
Understanding slope is crucial in many real-world applications. For example, civil engineers use slope to design roads and bridges, ensuring they are safe and efficient. Architects use slope to design roofs that effectively drain water. In finance, the slope of a stock's price trend can indicate its rate of growth or decline, helping investors make informed decisions. Even in everyday life, understanding slope helps us navigate hills and stairs more easily.
The slope of line AB, which contains points A(3, -2) and B(1, 8), is calculated to be -5 using the slope formula. Thus, the correct answer is option B: -5. This slope indicates a descending line as it moves from left to right.
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