Which equation in standard form has a graph that passes through the point (−4, 2)
 and has a slope of 92
 ?

To find the equation of a line in **standard form** (Ax + By = C) that passes through the point (-4, 2) with a slope of 92, we can follow these steps:

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

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

Where:
- \((x_1, y_1)\) is the point on the line, which is (-4, 2).
- \(m\) is the slope, which is 92.

Substitute the values:

\[
y - 2 = 92(x + 4)
\]

### Step 2: Simplify the equation
Expand the equation:

\[
y - 2 = 92x + 368
\]

Now, add 2 to both sides to get the equation in slope-intercept form:

\[
y = 92x + 370
\]

### Step 3: Convert to standard form
To convert the equation to standard form \(Ax + By = C\), move all terms to one side:

\[
-92x + y = 370
\]

Now, to make the leading coefficient positive, multiply the entire equation by -1:

\[
92x - y = -370
\]

This is the equation in standard form.

### Final Answer:
The equation of the line in standard form is:

\[
92x - y = -370
\]

Would you like more details or further explanation?

Here are five related questions to consider:
1. How do you derive the slope of a line from two given points?
2. What are the differences between point-slope form and slope-intercept form?
3. How do you find the x- and y-intercepts from an equation in standard form?
4. How do you convert from slope-intercept form to standard form?
5. Can a line with a slope of 0 have a standard form equation?

**Tip:** The coefficient of \(x\) in standard form should ideally be positive, so multiply the equation by -1 if necessary.

Which equation in standard form has a graph that passes through the point (−4, 2) and has a slope of 92?

Learn how to find the standard form of a line that passes through the point (-4, 2) and has a slope of 92. This step-by-step solution explains how to use the point-slope form and convert it to standard form. Suitable for students in Grades 8-10.

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