https://file.aiquickdraw.com/mathbot/file/1729643396581waer2d19.jpg

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.

Write an equation for the line shown on the graph below. Determine the equation in standard form.

Learn how to find the equation of a line in standard form given two points. This problem covers slope calculations and the transformation from point-slope to standard form, ideal for Grades 8-10 students.

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