Question

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4, -3)?

Given Line: y + 3 = 4(x + 4)

A. y + 3 = -4(x + 4)
B. y + 3 = 1(x + 4)
C. y + 3 = -11(x + 4)
D. y + 3 = 2(x + 4)
E. y + 3 = 4(x + 4)

Answer 1

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

Step-by-step explanation:

The given line has the equation y + 3 = 4(x + 4). To find the equation of the line that is perpendicular to this line and passes through the point (-4, -3), we need to determine the slope of the given line first. The slope-intercept form of a line is y = mx + b, where m is the slope. In this form, we can see that the slope of the given line is 4.

Since the line we are looking for is perpendicular to the given line, its slope will be the negative reciprocal of 4, which is -1/4. We can use this slope and the given point (-4, -3) to write the equation of the line in point-slope form: y - y1 = m(x - x1). Substituting the values, we get: y - (-3) = -1/4(x - (-4)).

Simplifying the equation gives us: y + 3 = -1/4(x + 4). So, the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4, -3) is option A: y + 3 = -4(x + 4).