Final answer:
To derive the equation of a line passing through (3, 4) and having intercepts of equal magnitude but opposite signs, understand that the slope is -1 and use point-slope form to obtain y = -x + 7 as the equation.
Step-by-step explanation:
The question is asking to find the equation of a line that passes through the point (3, 4) and has intercepts on the x and y axes that are equal in magnitude but opposite in sign.
This indicates that the x-intercept and y-intercept are of the form (a, 0) and (0, -a) respectively.
Firstly, since the x and y intercepts have the same absolute value, the slope of the line is -1.
The equation of a line with a slope m and passing through a point (x1, y1) can be written as (y - y1) = m(x - x1).
Substituting m = -1 and the point (3, 4), we get the equation (y - 4) = -1(x - 3), which simplifies to y = -x + 7.