Answer:
[tex]\large\boxed{\text{Table 1:}\ y=4x+1}\\\boxed{\text{Table 2:}\ y=\dfrac{1}{2}x-1}[/tex]
Step-by-step explanation:
Tables show linear functions.
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
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Table 1:
(0, 1) → b = 1, (1, 5)
[tex]m=\dfrac{5-1}{1-0}=\dfrac{4}{1}=4\\\\y=4x+1[/tex]
Table 2:
(4, 1), (6, 2)
[tex]m=\dfrac{2-1}{6-4}=\dfrac{1}{2}\\\\y=\dfrac{1}{2}x+b[/tex]
Put the coordinateso f the point (4, 1) to the equation of a line:
[tex]1=\dfrac{1}{2}(4)+b[/tex]
[tex]1=2+b[/tex] subtract 2 from both sides
[tex]-1=b\to b=-1[/tex]
[tex]y=\dfrac{1}{2}x-1[/tex]
