Final answer:
For line a, the equation is y = (-7/2)x + 11/2. For line b, the equation is y = (2/7)x + 6/7.
Step-by-step explanation:
To find the equation of line a, which is parallel to line TV, we need to find the slope of line TV. The equation of line TV is given as 7x + 2y - 3 = 0. To find the slope, we rearrange the equation to the form y = mx + b, where m is the slope. So, 2y = -7x + 3, y = (-7/2)x + 3/2. Therefore, line a will have the same slope of (-7/2) and the equation will be y = (-7/2)x + b. To find b, we substitute the coordinates of point P(-1,4): 4 = (-7/2)(-1) + b. Solving for b, we get b = 11/2. Therefore, the equation of line a is y = (-7/2)x + 11/2.
To find the equation of line b, which is perpendicular to line TV, we need to find the negative reciprocal of the slope of line TV. The slope of line TV is (-7/2), so the negative reciprocal is 2/7. Therefore, the equation of line b will have a slope of 2/7 and it will pass through point P(-1,4). Using the point-slope form, we have y - 4 = (2/7)(x - (-1)). Simplifying this equation, we get y - 4 = (2/7)(x + 1). Expanding and rearranging, the equation becomes y = (2/7)x + 6/7. Therefore, the equation of line b is y = (2/7)x + 6/7.