Consider line [tex]CD[/tex] passing through points [tex]C(-5,10)[/tex] and [tex]D(1,8)[/tex]. What is the slope of [tex]\overleftrightarrow{CD}[/tex]?
A. [tex]-\frac{1}{3}[/tex]
B. [tex]\frac{1}{3}[/tex]
C. 3
D. -3
Answer (1)
Use the slope formula: m = x 2 − x 1 y 2 − y 1 .
Substitute the coordinates of points C ( − 5 , 10 ) and D ( 1 , 8 ) into the slope formula: m = 1 − ( − 5 ) 8 − 10 .
Simplify the expression: m = 6 − 2 = − 3 1 .
The slope of the line C D is − 3 1 .
Explanation
Understanding the Slope Formula Let's find the slope of the line passing through the points C ( − 5 , 10 ) and D ( 1 , 8 ) . The slope formula is given by: m = x 2 − x 1 y 2 − y 1 where ( x 1 , y 1 ) and ( x 2 , y 2 ) are the coordinates of two points on the line.
Substituting the Coordinates Now, let's substitute the coordinates of points C and D into the slope formula. We have x 1 = − 5 , y 1 = 10 , x 2 = 1 , and y 2 = 8 . Plugging these values into the formula, we get: m = 1 − ( − 5 ) 8 − 10
Simplifying the Expression Next, we simplify the expression: m = 1 + 5 − 2 = 6 − 2 = − 3 1 So, the slope of the line C D is − 3 1 .
Final Answer Therefore, the slope of the line passing through points C ( − 5 , 10 ) and D ( 1 , 8 ) is − 3 1 .
Examples
Understanding slope is crucial in many real-world applications. For instance, when designing roads or ramps, engineers use the concept of slope to ensure they are not too steep for vehicles or people to navigate safely. A gentle slope, like -1/3, indicates a gradual decline, making it easier to ascend or descend. In construction, knowing the slope helps in proper drainage and preventing water accumulation.
