Final Answer:
The equation of the line passing through the point (5, -3) and parallel to the line 4y - x = 8 is y = 4x - 23. Option A is answer.
Step-by-step explanation:
Identify the slope of the parallel line:
The line 4y - x = 8 can be rearranged to slope-intercept form:
y = (1/4)x + 2
Therefore, the parallel line will have the same slope of 1/4.
Substitute the point (5, -3) into the point-slope equation:
The point-slope equation for a line with slope m passing through the point (x1, y1) is:
y - y1 = m(x - x1)
Substituting the values, we get:
y - (-3) = (1/4)(x - 5)
Solve for y:
y + 3 = (1/4)x - 5/4
y = (1/4)x - 23/4
Therefore, the equation of the parallel line is y = (1/4)x - 23/4, or simplified, y = 4x - 23.
Option A is answer.