a line includes the points (1,6) and (8,1). what is its equation in point - slope form? use one of the…

Explanation:

Step1: Calculate the slope

The formula for slope (m) between two points ((x_1,y_1)) and ((x_2,y_2)) is (m=\frac{y_2 - y_1}{x_2 - x_1}). Here, (x_1 = 1,y_1=6,x_2 = 8,y_2 = 1), so (m=\frac{1 - 6}{8 - 1}=\frac{-5}{7}).

Step2: Write the point - slope form

The point - slope form of a line is (y - y_1=m(x - x_1)). Using the point ((1,6)) and (m =-\frac{5}{7}), we get (y - 6=-\frac{5}{7}(x - 1)). Using the point ((8,1)) and (m =-\frac{5}{7}), we get (y - 1=-\frac{5}{7}(x - 8)).

Answer:

(y - 6=-\frac{5}{7}(x - 1)) or (y - 1=-\frac{5}{7}(x - 8))