9514 1404 393
Answer:
- y -6 = (-25/2)x
- y -13 = 5(x -2)
- y +4 = 10(x -2)
- not a linear relation
Step-by-step explanation:
The function will be linear if the differences in y-values are proportional to the differences in x-values. The constant of that proportionality is the slope of the line. A linear equation can be written using the point-slope form:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
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Table 1
x-differences: 2-0 = 2, 4-2 = 2, 6-4 = 2
y-differences: -19-6 = -25, -44-(-19) = -25, -69-(-44) = -25
m = -25/2; (h, k) = (0, 6)
linear relation: y -6 = (-25/2)x
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Table 2
x-differences: 2, 4, 2
y-differences: 10, 20, 10
m = 10/2 = 20/4 = 10/2 = 5; (h, k) = (2, 13)
linear relation: y -13 = 5(x -2)
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Table 3
x-differences: 2, 2, 2
y-differences: 20, 20, 20
m = 20/2 = 10; (h, k) = (2, -4)
linear relation: y +4 = 10(x -2)
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Table 4
x-differences: 2, 4, 2
y-differences: 25, 75, 125
not a linear relation
