Question

Which of the following is an equation of the line that passes through the point (-1, 4) and is perpendicular to the equation of the graph of y = 4x - 3?

A) y = 4x + 3
B) y = -4x - 3
C) y = -1/4x + 4
D) y = 4x - 1

Answer 1

The equation of the line that is perpendicular to y = 4x - 3 and passes through the point (-1, 4) is y = -1/4x + 4.

Step-by-step explanation:

The question asks about the equation of a line that is perpendicular to the given line y = 4x - 3 and passes through the point (-1, 4). To find a line perpendicular to another, we need to determine the negative reciprocal of the original line's slope. The slope of the given line is 4, so the slope of the perpendicular line is -1/4. We use this slope and the point (-1, 4) to find the perpendicular line's equation using the point-slope form y - y1 = m(x - x1), which after simplifying, provides the equation y = -1/4x + 4.