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The question asks for the equation in standard form that passes through the point \((-4, 2)\) and has a slope of \(\frac{9}{2}\).

To solve this:

### Step 1: Use the point-slope form of a line
The point-slope form of a line is given by:

\[
y - y_1 = m(x - x_1)
\]

where \((x_1, y_1)\) is a point on the line and \(m\) is the slope. Substituting the given point \((-4, 2)\) and slope \(\frac{9}{2}\):

\[
y - 2 = \frac{9}{2}(x + 4)
\]

### Step 2: Expand the equation
Now, expand the right side:

\[
y - 2 = \frac{9}{2}x + \frac{9}{2} \times 4
\]

\[
y - 2 = \frac{9}{2}x + 18
\]

### Step 3: Move the constants to one side
Add 2 to both sides:

\[
y = \frac{9}{2}x + 18 + 2
\]

\[
y = \frac{9}{2}x + 20
\]

### Step 4: Convert to standard form
The standard form of a linear equation is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers. To convert the equation \(y = \frac{9}{2}x + 20\) to standard form, we multiply through by 2 to eliminate the fraction:

\[
2y = 9x + 40
\]

Now rearrange to get the equation in standard form:

\[
9x - 2y = -40
\]

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

\[
9x - 2y = -40
\]

---

Would you like more details on any step or have any questions?

### 5 Related Questions:
1. How do you convert between slope-intercept and standard form?
2. What are the benefits of using the point-slope form?
3. Can you explain how to determine the slope given two points?
4. What defines the standard form of a linear equation?
5. How can you graph a line given its standard form equation?

### Tip:
To quickly check your equation, plug the given point into the final equation and ensure both sides are equal.

Which equation in standard form has a graph that passes through the point (-4, 2) and has a slope of 9/2?

Find the standard form of the equation that passes through the point (-4, 2) with a slope of 9/2. This linear equation problem covers key concepts like the point-slope form and converting to standard form. Suitable for students in Grades 9-10.

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