To solve the given problem, let's use the point-slope form equation of a line, which is given by:

$y - y_1 = m(x - x_1)$

Where:

• $m$ is the slope of the line
• $(x_1, y_1)$ is the given point through which the line passes.

Step-by-Step Solution:

1. Substitute the slope and point into the equation:

   • Slope ($m$) = 3
   • Point ($x_1, y_1$) = (-2, 4)

   Substituting into $y - y_1 = m(x - x_1)$:

   $y - 4 = 3(x - (-2))$

2. Simplify the equation:

   • $x - (-2)$ becomes $x + 2$

   So the equation becomes:

   $y - 4 = 3(x + 2)$

Match with the Options:

From the options, the correct answer is C: $y - 4 = 3(x + 2)$.

Would you like me to elaborate further on any step?

Related Questions:

1. How do you convert the point-slope form to slope-intercept form?
2. Can you explain the process of finding the equation of a line given two points?
3. What happens if the slope is zero or undefined?
4. How can you check if a given point lies on the line described by an equation?
5. What are the differences between point-slope form, slope-intercept form, and standard form?

Tip:

Always double-check the sign of the given point when substituting into the point-slope formula!