Question

A(5,23) and B (-2,2) are two points . Find the equation of a line AB

Answer 1

y = 3x + 8 is the equation of a line AB

Solution:

Given that,

A(5, 23)

B(-2, 2)

Find the slope of line

`m = (y_2-y_1)/(x_2-x_1)`

From given,

`(x_1, y_1) = (5, 23)\\\\(x_2, y_2) = (-2, 2)`

Substituting we get,

`m = (2-23)/(-2-5)\\\\m = (-21)/(-7)\\\\m = 3`

The equation of line in slope intercept form is:

y = mx + c ---------- eqn 1

Where,

m is the slope of line

c is the y intercept

Substitute m = 3 and (x, y) = (-2, 2) in eqn 1

2 = 3(-2) + c

2 = -6 + c

c = 8

Substitute c = 8 and m = 3 in eqn 1

y = 3x + 8

Thus the equation of line AB is found