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:
\(y-y_1=m(x-x_1)\)
Where m is equal to:
\(m=\frac{y_2-y_1}{x_2-x_1}\)
Additionally, the first point have the form \((x_1, y_1)\) and the second point have the form \((x_2,y_2)\).
Then, replacing the values of \(x_1\) by 2, \(y_1\) by 5, \(x_2\) by 6 and \(y_2\) by 9, we get:
\(m=\frac{9-5}{6-2}=1\)
Replacing the value of m and solving for y, we get:
\(y-5=1(x-2)\\y-5=x-2\\y=x-2+5\\y=x+3\)
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 )