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Social ScienceGiven the points (1,2) and (5, 50):a. Find a linear function of the form y = ax +b that goes through the two points.y 12x-10Editb. Find an exponential function of the form y = a - b* that goes through the two points.Round your answers to three decimal places.y a b*where a =and bc. Find a power function of the form y = ax2 that goes through the two points.y Edit
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Given the points (1,2) and (5, 50): a. Find a linear function of the form y = ax +b that goes through the two points. y 12x-10 Edit b. Find an exponential function of the form y = a - b* that goes through the two points. Round your answers to three decimal places. y a b*where a = and b c. Find a power function of the form y = ax2 that goes through the two points. y Edit
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(a) Consider the given two points on the line as (1,2) and (5,50). Note that, the equation of line passing through two points (x,,y) and (x,,y) is given by Hence, the calculate the equation of line from two points (1, 3) and (3, -3) as follows ( (x, 1;) = (1,2) (x,.y2)(5,50) y-2 50 2 x-1 5 1 -1 y-2 48 4 48 y-2 4 (x-1) y 12x-10
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(b) Consider the exponential function as y = ab*. Since the function passing through two points (1,2) and (5,50), the constant value can be obtained as follows ((x,y)(1.2) 1) 50 ab ((x, y)= (5,50)...(2) 2 ab 50 2b4 b 25 b 1.057 2 Substitute b 1.057 in the equation 2 ab and solve for a a(1.057) 2 2 1.892 = 1057 y =(1.892)(1.057) Thus the exponential function is where a 1.892 and b=1.057
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