Write the equation of the line shown in point-slope form. (2,1) (3,8)

Answer:The line equation that passes through the given points is 7x – y = 13 Explanation:Given:Two points are A(2, 1) and B(3, 8). To find:The line equation that passes through the given two points. Solution:We know that, general equation of a line passing through two points (x1, y1), (x2, y2) in point slope form is given by [tex]\frac{(y- y1)}{(x-x_1)}= \frac{((y_2- y_1)}{(x_2- x_1 )}[/tex][tex]{(y- y1)= \frac{((y_2- y_1)}{(x_2- x_1 )}\times(x-x_1)[/tex]..........(1) here, in our problem x1 = 3, y1 = 8, x2 = 2 and y2 = 1. Now substitute the values in (1) [tex](y-8) = \frac{(1 - 8)}{(2 - 3)}\times(x- 3)[/tex][tex](y -8) = \frac{(- 7)}{(-1)}(x-3)[/tex]y – 8 = 7(x – 3) y – 8 = 7x – 21  7x – y = 21 – 8  7x – y = 13  Hence, the line equation that passes through the given points is 7x – y = 13