Question

Write the standard form of the equation of the

line passing through the point (1, 5) and
perpendicular to the line 4x - 7y = -28.
[A] 7x+4y= 27
[B] -7x-4y = 27
[C] 4x+7y = 39
[D] 4x-7y = -39

Answer 1

The equation of the line perpendicular to 4x - 7y = -28 and passing through (1, 5) is 4x + 7y = 39, which is answer choice [C].

Step-by-step explanation:

The equation of the line passing through the point (1, 5) and perpendicular to the line 4x - 7y = -28 can be found by first determining the slope of the given line.

To find the perpendicular slope, we take the negative reciprocal of the original slope.

Since the original line has a slope of 4/7, the perpendicular slope will be -7/4. We then use the point-slope form to write the equation of the new line, y - y1 = m(x - x1), substituting the perpendicular slope for m, and the point (1, 5) for (x1, y1).

After simplifying, y - 5 = -7/4(x - 1), we can convert this into standard form by clearing the fractions and rearranging the terms which gives us 7x + 4y = 39. Therefore, the correct answer is [C] 4x + 7y = 39.