Find an equation for the linear function which has f(0.5)=0.8 and f(0.8)=−0.3

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lildeutsch11xq2j · Accepted Answer

Step 1&amp;nbsp;We have to find the linear function where,f(0.5)=0.8&amp;nbsp;and&amp;nbsp;f(0.8)=−0.3We know linear function form,f(x)=ax+bso we need to find a and b from the given conditions/Given&amp;nbsp;f(0.5)=0.8so putting&amp;nbsp;x=0.5&amp;nbsp;in&amp;nbsp;f(x)f(x)=ax+bf(0.5)=a×0.5+b0.8=0.5a+b0.5a+b=0.8.....(1)Also&amp;nbsp;f(0.8)=−0.3therefore putting&amp;nbsp;x=0.8&amp;nbsp;in&amp;nbsp;f(x),f(x)=ax+bf(0.8)=0.8a+b0.8a+b=−0.3&amp;nbsp;.....(2)Step 2Subtracting the corresponding parts of equation (1) and (2),0.5a−0.8a+b−b=0.8−(−0.3)−0.3a=0.8+0.3−0.3a=1.1a=−1.10.3=−113=−3.6Putting value of a in equation (1), we get0.5a+b=0.80.5×(−113)+b=0.8−5.53+b=0.8b=0.8+5.53=2.4+5.53=7.93=2.63Putting values of a and b in function,f(x)=ax+b=−3.6x+2.63Hence, liear function is&amp;nbsp;f(x)=−3.6x+2.63

Find an equation for the linear function which

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