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

To find the equation of a line in standard form, given that the line passes through the point (-4, 2) and has a slope of \( \frac{9}{2} \), we can follow these steps:

1. **Point-slope form**:
   The point-slope form of the equation of a line is:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( m \) is the slope and \( (x_1, y_1) \) is the point on the line.

   Plugging in \( m = \frac{9}{2} \), \( x_1 = -4 \), and \( y_1 = 2 \):
   \[
   y - 2 = \frac{9}{2}(x + 4)
   \]

2. **Simplify**:
   \[
   y - 2 = \frac{9}{2}(x + 4) = \frac{9}{2}x + \frac{9}{2} \times 4
   \]
   \[
   y - 2 = \frac{9}{2}x + 18
   \]

   Now, add 2 to both sides:
   \[
   y = \frac{9}{2}x + 20
   \]

3. **Convert to standard form**:
   Standard form is usually written as:
   \[
   Ax + By = C
   \]
   To convert, first multiply everything by 2 to eliminate the fraction:
   \[
   2y = 9x + 40
   \]

   Rearrange the terms:
   \[
   9x - 2y = -40
   \]

So, the equation of the line in standard form is:
\[
9x - 2y = -40
\]

Would you like a more detailed explanation of any step?

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Here are 5 related questions for further practice:
1. How would the equation change if the slope were \( -\frac{9}{2} \)?
2. What is the equation of a line parallel to this one but passing through a different point, say (3, -5)?
3. How do you find the y-intercept directly from the equation in standard form?
4. What would be the equation of a perpendicular line passing through (-4, 2)?
5. How does the standard form of an equation differ from the slope-intercept form?

**Tip**: Always clear fractions in linear equations by multiplying through by the denominator when converting to standard form.

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

Discover how to find the equation of a line in standard form that passes through the point (-4, 2) with a slope of 9/2. This step-by-step guide covers point-slope form and converting to standard form, ideal for students in Grades 9-10.

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