Question

Find the equation of the line / in the figure below. Give exact values using the form y = mx + b. m= b= f(x) = 10 х log 3

Answer 1

Answer 2

SOLUTION :

Curve : f(x) = y = 10^x 

Line : y  = m x + b

At points of intersections :

y (line) = y (curve)

=> m x + b = 10^x 

One point of intersection is at x = 0

So,

=> m * 0 + b = 10^0

=> b = 1 

So, line’s equation will be : y = m x + 1

At 2nd point of intersection , x = log (3)

So,

 m log (3) + 1 = 10^(log (3)) = 3

=> log (3) * m = 3 - 1 = 2

=> m = 2 / log (3)

Hence, equation of line will be :

y = 2 x / log (3)  + 1  (ANSWER).