To write a linear equation in standard form from a graph, just follow these simple steps.

Standard form looks like this:

$Ax + By = C$

Here, $A$, $B$, and $C$ are whole numbers, and $A$ should be positive.

Step 1: Find Two Points

First, pick at least two points from the graph.

For example, let’s say you find points $A(2, 3)$ and $B(4, 7)$.

Step 2: Calculate the Slope

Next, you'll need to find the slope using this formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So for our points:

$m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2$

This tells us that the slope $m$ is 2.

Step 3: Use Point-Slope Form

Now, let’s use the point-slope form of a line:

$y - y_1 = m(x - x_1)$

Using point $A(2, 3)$, we get:

$y - 3 = 2(x - 2)$

Step 4: Change to Standard Form

Next, we need to change this to standard form. Let’s simplify it:

Start with:

$y - 3 = 2x - 4$

Now, rearrange it to look like standard form:

$2x - y = 1$

Make sure $A$, $B$, and $C$ are whole numbers. They are in this case!

So, the final equation in standard form is:

$2x - y = 1$

Now you have your linear equation in standard form! Good job!