Question

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

Answer 1

The line equation that passes through the given points is 7x – y = 13

Step-by-step 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

`((y- y1))/((x-x_1))= (((y_2- y_1))/((x_2- x_1 ))`

`{(y- y1)= (((y_2- y_1))/((x_2- x_1 ))*(x-x_1)`..........(1)

here, in our problem x1 = 3, y1 = 8, x2 = 2 and y2 = 1.

Now substitute the values in (1)

`(y-8) = ((1 - 8))/((2 - 3))*(x- 3)`

`(y -8) = ((- 7))/((-1))(x-3)`

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