Question

Find the equation of the line going through the points (2,-1) and (5,2) 3x 2y

Answer 1

Answer:

The equation of the line is:

$y = x - 3$

Step-by-step explanation:

The general equation of a straight line is given by:

$y = ax + b$

Being given two points, we can replace x and y, solve the system and find the values for a and b.

Solution:

The line goes through the point $(2,-1)$. It means that when $x = 2, y = -1$. Replacing in the equation:

$y = ax + b$

$-1 = 2a + b$

$2a + b = -1$

The line also goes through the point $(5,2)$. It means that when $x = 5 y = 2$. Replacing in the equation:

$y = ax + b$

$2 = 5a + b$

$5a + b = 2$

Now we have to solve the following system of equations:

$1) 2a + b = -1$

$2) 5a + b = 2$

From 1), we have:

$b = -1 - 2a$

Replacing in 2)

$5a - 1 - 2a = 2$

$3a = 3$

$a = \frac{3}{3}$

$a = 1$

$b = -1 - 2a = -1 - 2 = -3$

The equation of the line is:

$y = x - 3$