Final answer:
The equation x - 4y = -4 (option c) represents the line parallel to the line through the points (-5, 2) and (3, 4) because it has the same slope of 1/4.
Step-by-step explanation:
To determine which line is parallel to the line containing the points (-5, 2) and (3, 4), we first find the slope of this line. The slope m is calculated by the formula (y2 - y1) / (x2 - x1). For the given points, the slope is (4 - 2) / (3 - (-5)) = 2 / 8 = 1 / 4. A line parallel to another has the same slope. Now, we transform the given equations into slope-intercept form, y = mx + b, and compare slopes.
- Equation a: x + 4y = 5 becomes 4y = -x + 5, and then y = -1/4x + 5/4 (slope is -1/4).
- Equation b: -4x + y = -2 becomes y = 4x - 2 (slope is 4).
- Equation c: x - 4y = -4 becomes -4y = -x - 4, and then y = 1/4x + 1 (slope is 1/4).
Only option c has the same slope of 1/4, therefore, the line represented by equation c, x - 4y = -4, is parallel to the line through the points (-5, 2) and (3, 4).