Final answer:
Using the slope-intercept form, the equation of the line passing through (3, -4) with a slope of 5 is y = 5x - 19.
Step-by-step explanation:
To write an equation for a line that passes through the point (3, -4) with a slope of 5 using the slope-intercept form, we must utilize the formula y = mx + b, where m is the slope and b is the y-intercept. Since we know the slope (m = 5) and a point on the line, we can find the y-intercept (b). Substituting the point into the equation, we get -4 = 5(3) + b. Solving for b gives us -4 = 15 + b, so b = -4 - 15 = -19, and the equation of the line is y = 5x - 19.