Final answer:
The equation of the line parallel to 14x + 7y = 49 and passing through the point (-5, -3) is found by first determining that the slope of the given line is -2. Since parallel lines have the same slope, the new line also has a slope of -2. Using the point-slope form with the given point and slope leads to the final equation y = -2x - 13.
Step-by-step explanation:
To write the equation of a line parallel to 14x + 7y = 49 that passes through the point (-5,-3), first find the slope of the given line by rewriting it in slope-intercept form (y = mx + b), where m is the slope. For the given line, dividing the entire equation by 7 yields y = -2x + 7, indicating that the slope (m) is -2. Since parallel lines have the same slope, the slope of our line is also -2. Next, utilize the point-slope form (y - y1 = m(x - x1)) with our point (-5, -3) and slope -2. This gives us y - (-3) = -2(x - (-5)), which simplifies to y + 3 = -2(x + 5). To get it into slope-intercept form, distribute the -2 and simplify, ending up with y = -2x -10 - 3, which gives us y = -2x - 13.
The final equation of the line parallel to 14x + 7y = 49 and passing through the point (-5, -3) is y = -2x - 13.