Find the slope of the line that contains (-1, 9) and (9, 9).
A. 10
B. 0
C. undefined
D. 9/5
Answer (2)
Identify the coordinates of the two points: ( − 1 , 9 ) and ( 9 , 9 ) .
Apply the slope formula: m = x 2 − x 1 y 2 − y 1 .
Substitute the coordinates into the formula: m = 9 − ( − 1 ) 9 − 9 .
Simplify to find the slope: m = 0 . The final answer is 0 .
Explanation
Understanding the Problem We are given two points (-1, 9) and (9, 9) and asked to find the slope of the line containing them.
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
Identifying Coordinates Let's identify the coordinates: x 1 = − 1 , y 1 = 9 x 2 = 9 , y 2 = 9
Calculating the Slope Now, substitute these values into the slope formula: m = 9 − ( − 1 ) 9 − 9 = 10 0 = 0
Final Answer Therefore, the slope of the line is 0.
Examples
Imagine you're cycling on a flat road. The slope represents how much you go up or down for every unit you move forward. If the slope is 0, it means the road is perfectly flat, and you're neither climbing nor descending. Understanding slope helps in many real-world scenarios, from designing roads and ramps to understanding graphs in science and economics.
The slope of the line that contains the points (-1, 9) and (9, 9) is 0, indicating that the line is horizontal. The calculation uses the slope formula and shows that there is no change in the y-coordinates. Therefore, the chosen answer is B. 0.
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