Determine which tow equations represent perpendicular line.

(a) y= 3/8 x -4
(b) y= 4x - 3/8
(c) y= - 1/4 x + 3/8
(d) y= 1/4 x - 3/8

b and c.

Perpendicular lines have slopes which are negative reciprocals of each other. So 4 and -1/4 work.

To determine which equations represent perpendicular lines, we need to compare their slopes. Perpendicular lines have slopes that are negative reciprocals of each other.

Let's compare the slopes of the given equations:

(a) y = 3/8 x - 4
The slope of this equation is 3/8.

(b) y = 4x - 3/8
The slope of this equation is 4.

(c) y = -1/4 x + 3/8
The slope of this equation is -1/4.

(d) y = 1/4 x - 3/8
The slope of this equation is 1/4.

To find the negative reciprocal of a slope, we simply flip the fraction and change the sign.

The negative reciprocal of 3/8 is -8/3.
The negative reciprocal of 4 is -1/4.
The negative reciprocal of -1/4 is 4.
The negative reciprocal of 1/4 is -4.

Comparing the slopes of the equations, we see that the equation (b) y = 4x - 3/8 has a slope of 4, which is the negative reciprocal of the slope -1/4 in equation (c) y = -1/4 x + 3/8.

Therefore, equations (b) and (c) represent perpendicular lines.

To determine which two equations represent perpendicular lines, we need to compare their slopes. Perpendicular lines have slopes that are negative reciprocals of each other.

First, let's determine the slope of each equation:

(a) y = 3/8x - 4
(b) y = 4x - 3/8
(c) y = -1/4x + 3/8
(d) y = 1/4x - 3/8

The slope of a linear equation in the form y = mx + b is represented by the coefficient of x (m).

For equation (a), the slope is 3/8.
For equation (b), the slope is 4.
For equation (c), the slope is -1/4.
For equation (d), the slope is 1/4.

Now, let's check which pairs of equations have slopes that are negative reciprocals of each other:

(a) and (b): The slopes are not negative reciprocals of each other.
(a) and (c): The slopes are not negative reciprocals of each other.
(a) and (d): The slopes are not negative reciprocals of each other.
(b) and (c): The slopes are negative reciprocals of each other.
(b) and (d): The slopes are not negative reciprocals of each other.
(c) and (d): The slopes are negative reciprocals of each other.

From the comparison, we can conclude that equations (b) and (c) represent perpendicular lines since their slopes are negative reciprocals of each other.

Therefore, the equations that represent perpendicular lines are:

(b) y = 4x - 3/8
(c) y = -1/4x + 3/8