Final answer:
The equation of a line parallel to 2x - 8y = 3 and passing through the point (8, -11) is x - 4y = -52.
Step-by-step explanation:
To find the equation of a line parallel to 2x - 8y = 3 that contains the point (8, -11), we need to find the slope of the given line and then use the point-slope form of a linear equation to find the equation of the parallel line.
The slope of the given line can be found by rearranging the equation into slope-intercept form y = mx + b, where m represents the slope. Solving for y, we get y = (1/4)x - 3/8. Therefore, the slope of the given line is 1/4.
Using the point-slope form of a linear equation, we can substitute the slope and the coordinates of the given point (8, -11) into the equation y - y1 = m(x - x1). After substituting the values, we get y + 11 = (1/4)(x - 8). Simplifying this equation further, we get x - 4y = -52.