Q:

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

Accepted Solution

A:
Answer:The equation of the line is:[tex]y = x - 3[/tex]Step-by-step explanation:The general equation of a straight line is given by:[tex]y = ax + b[/tex]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 [tex](2,-1)[/tex]. It means that when [tex]x = 2, y = -1[/tex]. Replacing in the equation:[tex]y = ax + b[/tex][tex]-1 = 2a + b[/tex][tex]2a + b = -1[/tex]The line also goes through the point [tex](5,2)[/tex]. It means that when [tex]x = 5 y = 2[/tex]. Replacing in the equation:[tex]y = ax + b[/tex][tex]2 = 5a + b[/tex][tex]5a + b = 2[/tex]Now we have to solve the following system of equations:[tex]1) 2a + b = -1[/tex][tex]2) 5a + b = 2[/tex]From 1), we have:[tex]b = -1 - 2a[/tex]Replacing in 2)[tex]5a - 1 - 2a = 2[/tex][tex]3a = 3[/tex][tex]a = \frac{3}{3}[/tex][tex]a = 1[/tex][tex]b = -1 - 2a = -1 - 2 = -3[/tex]The equation of the line is:[tex]y = x - 3[/tex]