how to find the equation of the line that passes through the given point and has the given slope: (-1, 7), m=-3

To find the equation of a line that passes through a given point and has a specified slope, you can use the **point-slope form** of a linear equation:

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

Where:
- \( (x_1, y_1) \) is the given point, which in your case is \( (-1, 7) \).
- \( m \) is the slope of the line, which is \( -3 \) in this case.

### Step-by-Step Solution:
1. Substitute the given point \( (-1, 7) \) and slope \( m = -3 \) into the point-slope formula:
   \[
   y - 7 = -3(x - (-1))
   \]
2. Simplify the equation:
   \[
   y - 7 = -3(x + 1)
   \]
3. Distribute the slope \( -3 \):
   \[
   y - 7 = -3x - 3
   \]
4. Add 7 to both sides to isolate \( y \):
   \[
   y = -3x - 3 + 7
   \]
   \[
   y = -3x + 4
   \]

### Final Answer:
The equation of the line is:
\[
y = -3x + 4
\]

Would you like more details on this process, or do you have any other questions?

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Here are 5 related questions you might find useful:
1. How do you convert the point-slope form into slope-intercept form?
2. What is the standard form of a line equation?
3. How do you find the slope of a line given two points?
4. How do you determine if two lines are parallel or perpendicular?
5. How do you graph a line using its equation?

**Tip:** When using the point-slope formula, carefully substitute the point coordinates and slope to avoid mistakes with signs.

How to find the equation of the line that passes through the given point and has the given slope: (-1, 7), m=-3

Learn how to find the equation of a line that passes through the point (-1, 7) with a slope of -3. This step-by-step solution explains how to apply the point-slope form to derive the equation, suitable for students in Grades 8-10.

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