To find the standard form equation of the line shown in the graph, we need to determine the slope and the y-intercept.

Step 1: Identify two points on the line.

From the graph, two points on the line are:

• $(0, 2)$ (y-intercept)
• $(2, 4)$

Step 2: Calculate the slope.

The formula for the slope $m$ is:

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

Using the points $(0, 2)$ and $(2, 4)$:

$m = \frac{4 - 2}{2 - 0} = \frac{2}{2} = 1$

So, the slope $m = 1$.

Step 3: Use the slope-intercept form to find the equation.

The slope-intercept form of a line is:

$y = mx + b$

Substitute the slope $m = 1$ and the y-intercept $b = 2$ into the equation:

$y = 1x + 2 \quad \text{or simply} \quad y = x + 2$

Step 4: Convert to standard form.

The standard form of a line is:

$Ax + By = C$

We can rearrange $y = x + 2$ into this form:

$x - y = -2$

So, the standard form equation of the line is:

$x - y = -2$

Do you have any questions or would you like further details?

Related questions:

1. How do you find the slope of a line from its graph?
2. What is the difference between slope-intercept form and standard form?
3. How can you convert from point-slope form to standard form?
4. What does the slope of 1 represent geometrically?
5. How do you find the y-intercept of a line given its equation?

Tip: When converting to standard form, it's often helpful to rearrange the equation so that all variables and constants are integers.