Calculate the slope of the line passing through the given points. If the slope is undefined, so state. Then indicate whether the line rises, falls, is horizontal, or is vertical. $(9,-5),(8,-5)
Answer (2)
Calculate the slope using the formula: m = x 2 − x 1 y 2 − y 1 .
Substitute the given points ( 9 , − 5 ) and ( 8 , − 5 ) into the formula: m = 8 − 9 − 5 − ( − 5 ) .
Simplify the expression: m = − 1 0 = 0 .
Since the slope is 0, the line is horizontal. Therefore, the answer is 0 .
Explanation
Understanding the Problem We are given two points, ( 9 , − 5 ) and ( 8 , − 5 ) , and we need to find the slope of the line passing through them. Then, we need to determine if the line rises, falls, is horizontal, or is vertical.
Using the Slope Formula The slope m 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 ) = ( 9 , − 5 ) and ( x 2 , y 2 ) = ( 8 , − 5 ) .
Calculating the Slope Substituting the given points into the slope formula, we get: m = 8 − 9 − 5 − ( − 5 ) = − 1 − 5 + 5 = − 1 0 = 0 So, the slope of the line is 0.
Determining the Line's Orientation Now, we need to determine if the line rises, falls, is horizontal, or is vertical.
If the slope is positive, the line rises.
If the slope is negative, the line falls.
If the slope is zero, the line is horizontal.
If the slope is undefined, the line is vertical. Since the slope is 0, the line is horizontal.
Conclusion Therefore, the slope of the line is 0, and the line is horizontal.
Examples
Imagine you are walking on a perfectly flat road. The road doesn't go uphill or downhill; it's completely level. This is similar to a horizontal line, which has a slope of zero. Understanding slopes helps in various real-life scenarios, such as designing roads, ramps, or roofs, ensuring they are safe and functional. For example, a builder needs to know the slope of a roof to ensure proper water runoff, or a civil engineer needs to calculate the slope of a road for safe vehicle operation.
The slope of the line through the points (9, -5) and (8, -5) is 0, indicating that the line is horizontal.
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