write the standard form of the equation of the line through the given point with the given slope
through : (-2,5), slope=-7/2

To write the standard form of the equation of a line, we begin with the **point-slope form** of the line equation:

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

Where:
- \((x_1, y_1)\) is the point through which the line passes
- \(m\) is the slope of the line.

Given:
- Point \((-2, 5)\)
- Slope \(m = -\frac{7}{2}\)

Substitute these values into the point-slope form:

\[
y - 5 = -\frac{7}{2}(x + 2)
\]

Now, we'll simplify and convert this equation into standard form, \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\) is positive.

1. Distribute the slope on the right-hand side:
   \[
   y - 5 = -\frac{7}{2}x - 7
   \]

2. Add 5 to both sides:
   \[
   y = -\frac{7}{2}x - 7 + 5
   \]
   \[
   y = -\frac{7}{2}x - 2
   \]

3. To eliminate the fraction, multiply every term by 2:
   \[
   2y = -7x - 4
   \]

4. Rearrange the terms to put the equation in standard form:
   \[
   7x + 2y = -4
   \]

Thus, the standard form of the equation is:

\[
7x + 2y = -4
\]

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Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the slope of a line given two points?
2. Can you convert a standard form equation to slope-intercept form?
3. What does the slope of a line represent geometrically?
4. How do you determine if two lines are parallel or perpendicular based on their slopes?
5. How can we use standard form equations to find intercepts?

**Tip:** Always check the equation in standard form to ensure the leading coefficient \(A\) is positive and all fractions are cleared.

write the standard form of the equation of the line through the given point with the given slope through: (-2,5), slope=-7/2

Learn how to convert the point-slope form of a line equation to standard form. This problem, through the point (-2, 5) with slope -7/2, is solved step-by-step and covers linear equations and algebraic techniques. Suitable for Grades 8-10.

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