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.