The slope for the line with points (-1, 5) and (2, 0) is True or False?
Answer (2)
Calculate the slope using the formula: s l o p e = x 2 − x 1 y 2 − y 1 .
Substitute the given points (-1, 5) and (2, 0) into the formula: s l o p e = 2 − ( − 1 ) 0 − 5 .
Simplify the expression: s l o p e = 3 − 5 .
The slope of the line is − 3 5 , so the answer is T r u e .
Explanation
Understanding the Problem We are given two points, (-1, 5) and (2, 0), and we need to determine if the statement about the slope of the line passing through these points is true or false.
Finding the Slope To find the slope of a line passing through two points ( x 1 , y 1 ) and ( x 2 , y 2 ) , we use the formula: s l o p e = x 2 − x 1 y 2 − y 1 In this case, ( x 1 , y 1 ) = ( − 1 , 5 ) and ( x 2 , y 2 ) = ( 2 , 0 ) .
Calculating the Slope Plugging in the coordinates into the slope formula, we get: s l o p e = 2 − ( − 1 ) 0 − 5 = 2 + 1 − 5 = 3 − 5 So, the slope of the line is − 3 5 .
Determining if the Statement is True or False The question asks whether the slope for the line with points (-1, 5) and (2, 0) is a certain value. Since the value is not specified in the question, let's assume the question is asking if the slope is − 3 5 . If the question asks if the slope is − 3 5 , then the statement is True.
Conclusion Therefore, the slope of the line passing through the points (-1, 5) and (2, 0) is indeed − 3 5 .
Examples
Understanding the slope of a line is crucial in many real-world applications. For example, in construction, the slope of a ramp determines its steepness, affecting accessibility. In economics, the slope of a supply or demand curve indicates how sensitive the quantity supplied or demanded is to changes in price. Calculating slopes helps engineers design safe and efficient structures and helps economists understand market behavior.
The slope of the line through the points (-1, 5) and (2, 0) is calculated as -5/3. If the question asks if this calculated slope is correct, the answer is True. Thus, the slope for the line is indeed -5/3.
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