The exponential equation that matches the coordinate is 3(2)^x while the linear equation is y = 6x
Exponential equation
The standard exponential equation is expressed as y= ab^x
where
a is the base
x is the exponent
Given the coordinates (2, 12) and (4, 48)
12 = ab^2
48 = ab^4
Find the ratio
4 = b^2
b = 2
Sice ab^2 = 12
4a = 12
a = 3
The exponential equation that matches the coordinate is 3(2)^x
For the linear equation
The standard form is y = mx + b
m is the slope = 48-12/4-2
Slope = 12/2
Slope = 6
For the y-intercept
12 = 6(2) + b
b = 0
Hence the required linear equation is. y = 6x
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