Final answer:
To find the equation of a line parallel to 2x - 8y = 3 that goes through the point (8, -11), we determine the slope of the original line and use it to write the equation of the parallel line. After calculating the y-intercept, we find that the correct equation is x - 4y = -52 (answer choice B).
Step-by-step explanation:
The question asks for the equation of a line that is parallel to a given line and passes through a given point. The original line has the equation 2x - 8y = 3. To find a parallel line, we need a line with the same slope. We can first rewrite the given equation in slope-intercept form (y = mx + b) to determine its slope.
By rearranging the equation, we get y = (1/4)x - (3/8). The slope (m) is therefore 1/4. A parallel line must have the same slope, so it will be in the form y = (1/4)x + b. To find the y-intercept (b), we'll plug in the coordinates of the given point (8, -11) into this equation: -11 = (1/4)(8) + b, which simplifies to -11 = 2 + b. Solving for b gives us b = -13.
Therefore, the equation of the desired line is y = (1/4)x - 13. To match the form of the given answer choices, we multiply through by 4 to get 4y = x - 52. Rearranging terms gives us x - 4y = 52, which corresponds to answer choice B: x - 4y = -52.