Final answer:
The calculated equation for the line perpendicular to the given line 4x + y = 3 and passing through the point (4, -3) is y = (1/4)x - 4. However, none of the multiple-choice answers correspond to this equation, suggesting there might be an error in the question or answer choices.
Step-by-step explanation:
To find an equation of a line that is perpendicular to another, we first need to know the slope of the original line. The given line is 4x + y = 3. Let's solve for y: y = -4x + 3. This equation is in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope (m) is -4. A line perpendicular to this one will have a slope that is the negative reciprocal of -4, which is 1/4 or 0.25.
The next step is to use the point (4, -3) that the perpendicular line must pass through, along with the perpendicular slope, to find the equation of the line. Using the point-slope formula, which is y - y1 = m(x - x1), with (x1, y1) being the point (4, -3) and m being 1/4, we get:
y - (-3) = 1/4(x - 4)
Now, let's simplify and put this into slope-intercept form (y = mx + b):
y + 3 = 1/4x - 1
y = 1/4x - 1 - 3
y = 1/4x - 4
This equation can be further simplified to match one of the multiple-choice options by multiplying both sides by 4 to remove the fraction:
4y = x - 16
y = (1/4)x - 4
Comparing this to the multiple-choice options, it is clear that none of the provided options correctly represents the perpendicular line with the point (4, -3). Therefore, there may be a typo in the question or the options provided.