Question

Line GH passes through points (2, 5) and (6, 9). Which equation represents line GH?

Answer 1

The equation that represent the line GH is:

y = x + 3

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=(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=(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 )