A line has a slope of $-\frac{3}{5}$. Which ordered pairs could be points on a parallel line? Select two options. A. $(-8,8)$ and $(2,2)$ B. $(-5,-1)$ and $(0,2)$ C. $(-3,6)$ and $(6,-9)$ D. $(-2,1)$ and $(3,-2)$ E. $(0,2)$ and $(5,5)
Answer (2)
Calculate the slope between each pair of points using the formula m = x 2 − x 1 y 2 − y 1 .
Check if the calculated slope is equal to − 5 3 for each pair.
Identify the pairs with a slope of − 5 3 :
(-8, 8) and (2, 2)
(-2, 1) and (3, -2)
The two pairs of points that could be on a line parallel to the given line are (-8, 8) and (2, 2), (-2, 1) and (3, -2) .
Explanation
Understanding the Problem The problem states that we need to find two pairs of ordered pairs that could be points on a line parallel to a line with a slope of − 5 3 . Parallel lines have the same slope. Therefore, we need to calculate the slope between each pair of given points and check if it equals − 5 3 which is equal to -0.6.
Stating the Slope Formula We will use the slope formula to calculate the slope between two points ( x 1 , y 1 ) and ( x 2 , y 2 ) , which is given by: m = x 2 − x 1 y 2 − y 1
Calculating Slopes
Pair 1: (-8, 8) and (2, 2) m = 2 − ( − 8 ) 2 − 8 = 10 − 6 = − 5 3 = − 0.6 The slope is -0.6, which is equal to − 5 3 .
Pair 2: (-5, -1) and (0, 2) m = 0 − ( − 5 ) 2 − ( − 1 ) = 5 3 = 0.6 The slope is 0.6, which is not equal to − 5 3 .
Pair 3: (-3, 6) and (6, -9) m = 6 − ( − 3 ) − 9 − 6 = 9 − 15 = − 3 5 = − 1.666... The slope is approximately -1.67, which is not equal to − 5 3 .
Pair 4: (-2, 1) and (3, -2) m = 3 − ( − 2 ) − 2 − 1 = 5 − 3 = − 0.6 The slope is -0.6, which is equal to − 5 3 .
Pair 5: (0, 2) and (5, 5) m = 5 − 0 5 − 2 = 5 3 = 0.6 The slope is 0.6, which is not equal to − 5 3 .
Identifying Parallel Lines The pairs that have a slope of − 5 3 are:
(-8, 8) and (2, 2)
(-2, 1) and (3, -2)
Therefore, these two pairs of points could be on a line parallel to the given line.
Final Answer The ordered pairs that could be points on a parallel line are:
(-8, 8) and (2, 2)
(-2, 1) and (3, -2)
Examples
Understanding parallel lines is crucial in architecture and design. For instance, when designing a building, architects ensure that walls are parallel to each other for structural stability and aesthetic appeal. Similarly, in urban planning, streets are often designed to be parallel to optimize traffic flow and land use. The concept of parallel lines and their slopes helps in creating accurate blueprints and layouts, ensuring that structures are aligned correctly and efficiently.
The ordered pairs that could be points on a line parallel to a line with a slope of − 5 3 are the pairs in A: (-8, 8) and (2, 2) and D: (-2, 1) and (3, -2).
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