https://file.aiquickdraw.com/mathbot/file/17301601111945ptlrpuo.jpg

To solve this problem, let's use the **point-slope form** of a line, given by:

\[
y - y_0 = m(x - x_0)
\]

where:
- \( (x_0, y_0) = (4, 10) \) is the point given in the problem,
- \( m = -7 \) is the slope.

### Step-by-Step Solution:

1. Substitute the values into the formula:
   \[
   y - 10 = -7(x - 4)
   \]

2. Distribute the slope \( -7 \) through the parentheses:
   \[
   y - 10 = -7x + 28
   \]

3. Add \( 10 \) to both sides to solve for \( y \):
   \[
   y = -7x + 28 + 10
   \]
   \[
   y = -7x + 38
   \]

### Final Answer:
The equation in point-slope form is:
\[
y = -7x + 38
\]

Would you like further clarification or additional help on this problem?

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### Related Questions:
1. What is the general formula for the point-slope form of a line?
2. How would you convert a point-slope form equation to slope-intercept form?
3. How does changing the slope value affect the graph of the line?
4. How do you find the y-intercept from a point-slope form equation?
5. What are the conditions for two lines to be parallel or perpendicular?

### Tip:
To avoid sign errors, carefully distribute negative slopes and double-check your calculations when substituting into formulas.

Write an equation for the line through the point (4, 10) with slope -7 in point-slope form.

Find the equation of a line passing through the point (4, 10) with a slope of -7, using the point-slope form formula y - y0 = m(x - x0). This problem covers fundamental concepts in linear equations, perfect for students in Grades 8-10.

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