1. Use the point-slope form of the equation of a line:
y - y_1 = m(x - x_1)
2. Substitute the given point (3, -4) and the slope m = 3 into the point-slope form:
y - (-4) = 3(x - 3)
3. Simplify the equation:
y + 4 = 3x - 9
4. Subtract 4 from both sides to find the equation in slope-intercept form:
y = 3x - 13
5. The main equation of the line is:
y = 3x - 13