Final answer:
To find the equation of a line parallel to the given line, determine the slope of the given line and use the point-slope form to find the equation of the parallel line. The equation of the parallel line in general form is 4x + 27y + 298 = 0.
Step-by-step explanation:
To find the equation of a line parallel to the given line, we need to determine the slope of the given line first. The given line has the equation 4x+27y−5=0. Rearranging this equation, we get 27y = -4x + 5 and dividing both sides by 27, we find that y = -4/27x + 5/27. So, the slope of the given line is -4/27.
Since the parallel line must have the same slope, we can use the point-slope form of a line to find its equation. Using the point (-7, -10) and the slope -4/27, we have: y + 10 = -4/27(x + 7). Simplifying this equation, we get y + 10 = -4/27x - 28/27. Multiplying through by 27, we obtain the equation 27y + 270 = -4x - 28. Rearranging, we get 4x + 27y + 298 = 0. Therefore, the equation of the parallel line in general form is 4x + 27y + 298 = 0.