What is the equation of a line that passes through the points of the arithmetic sequnce u0 10 un-1 -3 where n 1?

Answer 1

To find the equation of the line that passes through the points of the arithmetic sequence defined by ( u_0 = 10 ) and ( u_{n-1} = -3 ) where ( n = 1 ), we first identify the two points: ( (0, 10) ) and ( (1, -3) ). The slope ( m ) of the line between these points is calculated as ( m = \frac{-3 - 10}{1 - 0} = -13 ). Using the point-slope form ( y - y_1 = m(x - x_1) ), we can write the equation as ( y - 10 = -13(x - 0) ), simplifying to ( y = -13x + 10 ).