Question: 1. Write an equation of the line that is parallel to y = -4x + 8 and passes through the point (5, 1).
2. Write an equation of the line that is perpendicular to y = -4x + 8 and passes through the point (5,1).

Explanation is written below.

Step-by-step explanation:

                                                1)

Given the line

Comparing with the slope-intercept form of the line equation

Where m is the slope and b is the y-intercept

So, the slope of the line = m = -4

Thus, the equation of the line that is parallel to y = -4x + 8 and passes through the point (5, 1), using point slope form

Here, m is the slope and (x₁, y₁) is the point

substituting the values m = -4 and the point (5, 1)

y-1 = -4 (x - 5)

y-1 = -4x+20

y = -4x+20+1

y = -4x + 21

                                                    2)

Given the equation

Comparing with the slope-intercept form of the line equation

Where m is the slope and b is the y-intercept

So, the slope of the line = m = -4

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

The slope of the perpendicular line will be: 1/4

Thus, an equation of the line that is perpendicular to y = -4x + 8 and passes through the point (5,1), using point slope form

Here, m is the slope and (x₁, y₁) is the point

substituting the values m = 1/4 and the point (5, 1)

Add 1 to both sides