Question

Tell whether the lines y=-4x+3 and -2x+8y=5 are parallel, perpendicular, or neither.

Answer 1

Answer:

The lines are perpendicular to each other.

Step-by-step explanation:

Given equations of lines:

1. $y=-4x+3$

2. $-2x+8y=5$

Writing equation both equations in slope-intercept form which is

$y=mx+b$

where $m$ represents slope and $b$ represents y-intercept.

1. $y=-4x+3$

This is already in slope-intercept form.

The slope of the line

$m_1=-4$

2. $-2x+8y=5$

Adding $2x$ both sides.

$-2x+8y+2x=2x+5$

$8y=2x+5$

Dividing both sides by 8.

$\frac{8y}{8}=\frac{2x+5}{8}$

$y=\frac{2x+5}{8}$

Splitting denominators.

$y=\frac{2x}{8}+\frac{5}{8}$

Simplifying fraction.

$y=\frac{1}{4}x+\frac{5}{8}$

So, for the line the slope is.

$m_2=\frac{1}{4}$

A) Checking for parallel.

For parallel lines the slopes of the line are equal.

Since $m_1\neq m_2$

So, lines are not parallel.

B) Checking for perpendicular.

For perpendicular line the slopes of the line are related as:

$m_1\times m_2=-1$

Finding the product of the slopes to check weather it equals -1.

$-4\times\frac{1}{4}$

⇒ $-1$

The condition for perpendicular lines is satisfied as the product of the slopes =-1

Hence, the lines are perpendicular to each other.