Question

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

Answer 1

I'm pretty sure that the equation is y=x+3

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Answer 2

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 )