Question

2. ) Write an equation of the line that is perpendicular to the line y = 4x - 10 that passes through the point (-16, 2).

A) y = -1/4 x - 2


B) y - 4 x + 6


C) y = -1/4 x + 2


D) y-4 x +2


3) Find the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)



A) y = -3x + 2


B) y = -3x + 3


C) y = -1/3x + 2


D) y = -1/3x + 3


4) Consider the line in the coordinate plane that passes through the point (-5, 2) and the origin. Find the slope of a line perpendicular to the line described


A) -2/5

B) -5/2

C) 1/2

D) 5/2

Answer 1

2) The negative reciprocal of 4 is -1/4.

Using the point-slope form of a line (y - y1 = m(x - x1)), where (x1, y1) is the given point (-16, 2) and m is the slope:

y - 2 = -1/4(x - (-16))

y - 2 = -1/4(x + 16)

y - 2 = -1/4x - 4

y = -1/4x - 2

Therefore, the equation of the line perpendicular to y = 4x - 10 that passes through the point (-16, 2) is y = -1/4x - 2. So, the correct answer is A.

3) The given equation is y - 3x = -8. To find the equation of a line perpendicular to this, we need to determine the negative reciprocal of the slope of the given line, which is 3. The negative reciprocal of 3 is -1/3.

Using the point-slope form with the point (3, 2) and the slope -1/3:

y - 2 = -1/3(x - 3)

y - 2 = -1/3x + 1

y = -1/3x + 3

Therefore, the equation of the line perpendicular to y - 3x = -8 that passes through the point (3, 2) is y = -1/3x + 3. So, the correct answer is D.

4) The given line passes through the point (-5, 2) and the origin (0, 0). The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1).

slope = (0 - 2) / (0 - (-5))

slope = -2 / 5

slope = -2/5

The negative reciprocal of -2/5 is 5/2. Therefore, the slope of a line perpendicular to the line passing through (-5, 2) and the origin is 5/2. So, the correct answer is D.