Answer:
The equation that represent the line GH is:
y = x + 3
Step-by-step explanation:
If we have two point of a line, we can calculate the equation that represent the line using the following equation:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is equal to:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Additionally, the first point have the form [tex](x_1, y_1)[/tex] and the second point have the form [tex](x_2,y_2)[/tex].
Then, replacing the values of [tex]x_1[/tex] by 2, [tex]y_1[/tex] by 5, [tex]x_2[/tex] by 6 and [tex]y_2[/tex] by 9, we get:
[tex]m=\frac{9-5}{6-2}=1[/tex]
Replacing the value of m and solving for y, we get:
[tex]y-5=1(x-2)\\y-5=x-2\\y=x-2+5\\y=x+3[/tex]
So, the equation that represent Line GH is:
y = x + 3
That means that every point of the line GH have the following form:
( x , y ) = ( x , x+3 )
