Find an equation of the line passing through the given point

Find an equation of the line passing through the given points. Use function notation to write the equation, (-1,3) and (0,1) f(x) =

Solution

Let the equation of the required line be y = f(x) = mx + c where m is the slope and c is the y-intercept. Since this line passes through the points ( -1,3) and (0,1) , its slope is (3 -1)/ (-1 -0) = -2. Then the line\'s equation changes to y = f(x) = -2x +c. Further, on substituting x = 0 and y 1 in the equation of the line, we get 1= -2*0 +c or, c = 1. Then the equation of the line is f(x) = -2x +1. We can verify the result by checking whether the point ( -1,3) lies on this line.Since, -2(-1) + 1 = 2 + 1 = 3, the point (-1,3) lies on this line. Hence the required equation is f(x) = -2x + 1.