Which equation in standard form has a graph that passes through the point (−4, 2)(−4, 2) and has a slope of 9292 ?

A.9x−2y=369x−2y=36

B.9x−2y=269x−2y=26

C.9x−2y=−409x−2y=−40

D.9x−2y=−109x−2y=−10


To determine which equation in standard form represents the line that passes through the point \((-4, 2)\) and has a slope of \(\frac{9}{2}\), we need to use the point-slope form of the equation of a line and convert it to standard form.

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

2. Substituting \((x_1, y_1) = (-4, 2)\) and \(m = \frac{9}{2}\) into the point-slope form:
   \[ y - 2 = \frac{9}{2}(x + 4) \]

3. Simplify and convert to slope-intercept form:
   \[ y - 2 = \frac{9}{2}x + \frac{9}{2} \cdot 4 \]
   \[ y - 2 = \frac{9}{2}x + 18 \]
   \[ y = \frac{9}{2}x + 18 + 2 \]
   \[ y = \frac{9}{2}x + 20 \]

4. Convert to standard form \(Ax + By = C\):
   \[ y = \frac{9}{2}x + 20 \]
   Multiply every term by 2 to eliminate the fraction:
   \[ 2y = 9x + 40 \]
   Rearrange to standard form:
   \[ 9x - 2y = -40 \]

Thus, the correct equation in standard form is:
\[ 9x - 2y = -40 \]

So, the correct answer is:
**C. 9x - 2y = -40**

Would you like details or have any questions? 

Here are 5 related questions to expand your understanding:
1. How do you convert an equation from slope-intercept form to standard form?
2. What is the point-slope form of a line, and when is it useful?
3. Can you explain the process of finding the slope of a line given two points?
4. How do you determine if a point lies on a given line?
5. What are the differences between different forms of linear equations (slope-intercept, point-slope, standard)?

**Tip:** Always check your work by substituting the given point into your final equation to ensure it satisfies the equation.

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

Learn 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 problem covers key concepts like point-slope form and the conversion to standard form. Suitable for students in Grades 9-11.

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