Determine if the tables and graphs below express a direct variation between the variables If they do, find the constant of variation and an equation that defines the relation. 1. 2. 3. 4. 5. 6. X y X y X y X y X y X y 1 -3 7 14 -21 -28 3 6₁ -9 -12 -15 10 -20 25 -3 2 -4 5 2 1 2 3 4 -6 -9 -12 16 12 6 7 3 4 2 3 20 15 8 9 5 4 24 28 18 21 10 11 12 13 32 24 82

Question

Determine if the tables and graphs below express a direct variation between the variables If they do, find the constant of variation and an equation that defines the relation. 1. 2. 3. 4. 5. 6. X y X y X y X y X y X y 1 -3 7 14 -21 -28 3 6₁ -9 -12 -15 10 -20 25 -3 2 -4 5 2 1 2 3 4 -6 -9 -12 16 12 6 7 3 4 2 3 20 15 8 9 5 4 24 28 18 21 10 11 12 13 32 24 82​

verdadseankenji · Answer

Answer:To determine if the tables and graphs express a direct variation between the variables, we need to check if the ratio of y-values to x-values remains constant. If the ratio is constant, then there is a direct variation between the variables.Let's analyze each set of values:1. X    y   1    -3   2    -4The ratio of y-values to x-values is (-3)/1 = -4/2 = -2. Since the ratio is constant, there is a direct variation. The constant of variation can be found by taking any x-y pair, for example, (1, -3), and dividing y by x: -3/1 = -3. Therefore, the equation that defines the relation is y = -3x.2. X     y   7     14   5     10The ratio of y-values to x-values is 14/7 = 10/5 = 2. The ratio is constant, indicating a direct variation. The constant of variation is found by taking any x-y pair, such as (7, 14), and dividing y by x: 14/7 = 2. Therefore, the equation that defines the relation is y = 2x.3. X     y   -21  -28   -15  -20The ratio of y-values to x-values is (-28)/(-21) = (-20)/(-15) = 4/3. The ratio is constant, indicating a direct variation. The constant of variation is found by taking any x-y pair, such as (-21, -28), and dividing y by x: -28/(-21) = 4/3. Therefore, the equation that defines the relation is y = (4/3)x.4. X     y   -9    -12   -6    -9The ratio of y-values to x-values is (-12)/(-9) = (-9)/(-6) = 4/3. The ratio is constant, indicating a direct variation. The constant of variation is found by taking any x-y pair, such as (-9, -12), and dividing y by x: -12/(-9) = 4/3. Therefore, the equation that defines the relation is y = (4/3)x.5. X     y   -20  -3   -12  -6The ratio of y-values to x-values is (-3)/(-20) = (-6)/(-12) = 1/4. The ratio is not constant, indicating that there is no direct variation between the variables.6. X     y   -15  -9   -10  -6The ratio of y-values to x-values is (-9)/(-15) = (-6)/(-10) = 3/5. The ratio is not constant, indicating no direct variation between the variables.In summary, the tables and graphs that express direct variation are 1 and 2. The equations that define the relations are:1. y = -3x2. y = 2x

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