find the linear interpolating polynomial which passes through the points :(0,+1),(1,0)?

Answer 1

The equation to the straight line going through these 2 points is of the form y = mx + c.
By substituting the two points into this equation, separately,
we can find the value of m and c.
First point is (0,1), so the equation is 1 = m*0 + c, from which we get c = 1.
Second point is (1,0), so the equation is 0 = m*1 + c, or m = -c, but c = 1, so m = -1.
After substituting m = -1 and c = 1 into y = mx + c,
the equation to the line is thus y = -x + 1.