To determine the equation of the line shown in the graph, let's follow these steps:

1. Identify two points on the line:

From the image, we can see two points clearly marked:

• Point 1: $(-3, -2)$
• Point 2: $(3, 5)$

2. Calculate the slope of the line:

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

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

Substituting the coordinates of the points:

$m = \frac{5 - (-2)}{3 - (-3)} = \frac{7}{6}$

So, the slope of the line is $\frac{7}{6}$.

3. Use the point-slope form of the equation of a line:

The point-slope form is:

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

Let's use the point $(-3, -2)$ and the slope $\frac{7}{6}$:

$y + 2 = \frac{7}{6}(x + 3)$

4. Simplify and convert to standard form:

Expand and simplify the equation:

$y + 2 = \frac{7}{6}x + \frac{7}{2}$

Multiply through by 6 to eliminate the fractions:

$6y + 12 = 7x + 21$

Rearrange the terms to get the equation in standard form $Ax + By = C$:

$7x - 6y = -9$

Thus, the equation of the line in standard form is:

$7x - 6y = -9$

Would you like further clarification on any part of this process?

Here are five follow-up questions for practice:

1. What is the general form of the point-slope equation?
2. How do you interpret the slope in terms of rise over run?
3. What is the difference between slope-intercept form and standard form?
4. How can you determine the x- and y-intercepts from the standard form of a line equation?
5. How would you solve for the slope if given only a graph without labeled points?

Tip: Always verify points by substituting them back into the final equation to check for correctness.