Final answer:
To find the equations of lines a and b, we first identify the slope of the given line l, then find the parallel slope for line a and the perpendicular slope for line b, and use point P(-4, 4) to determine the y-intercepts.
Step-by-step explanation:
The question asks for the equations of two lines, a and b, where line a is parallel to line l, and line b is perpendicular to line l. Line l is given by the equation -4x + 2y - 3 = 0.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. The slope of line l can be found by rearranging its equation to the slope-intercept form, which is y = 2x + 1.5. Since line a is parallel to line l, it will have the same slope, which is 2. Using the point P(-4, 4), we can determine the y-intercept for line a, resulting in the equation y = 2x + 12.
For the perpendicular line b, we need a slope that is the negative reciprocal of the slope of line l. The negative reciprocal of 2 is -1/2. Again, using point P(-4, 4), we get the equation of line b as y = -1/2x + 6.