https://file.aiquickdraw.com/mathbot/file/172702992595227hdvhpc.jpg

The question asks how to use the slope formula to write the equation of a line that passes through the point \( (3, -2) \) and has a slope of 4. To answer this, let's break it down using the slope-intercept form of a line.

### Step-by-Step Solution:

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

2. **Given Values**: From the problem:
   - The slope \( m = 4 \).
   - The point is \( (3, -2) \), so \( x_1 = 3 \) and \( y_1 = -2 \).

3. **Substitute**: Substitute the values into the formula:
   \[
   y - (-2) = 4(x - 3)
   \]
   Simplifying:
   \[
   y + 2 = 4(x - 3)
   \]

4. **Final Equation**: To put this in the form of \( y = mx + b \), distribute the slope:
   \[
   y + 2 = 4x - 12
   \]
   Subtract 2 from both sides:
   \[
   y = 4x - 14
   \]

Thus, the equation of the line is:
\[
y = 4x - 14
\]

### Answer to Fill-in-the-Blanks:
- Substitute **4** for \( m \),
- Substitute **3** for \( x_1 \),
- Substitute **-2** for \( y_1 \).

Would you like more details on any part of the process?

### Related Questions:
1. What is the general form of the equation of a line?
2. How do you convert point-slope form to slope-intercept form?
3. How would you find the equation of a line if given two points?
4. What is the meaning of the slope in a line equation?
5. How does the slope affect the steepness and direction of a line?

### Tip:
Always remember to simplify your equation after substituting values into the point-slope formula to get the final slope-intercept form.

Explain how you can use the slope formula to write an equation of the line that passes through (3, -2) and has a slope of 4.

Learn how to write the equation of a line that passes through the point (3, -2) and has a slope of 4. This problem uses the point-slope form of a line equation and simplifies it into slope-intercept form. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation