Answer:
The lines are perpendicular to each other.
Step-by-step explanation:
Given equations of lines:
1. [tex]y=-4x+3[/tex]
2. [tex]-2x+8y=5[/tex]
Writing equation both equations in slope-intercept form which is
[tex]y=mx+b[/tex]
where [tex]m[/tex] represents slope and [tex]b[/tex] represents y-intercept.
1. [tex]y=-4x+3[/tex]
This is already in slope-intercept form.
The slope of the line
[tex]m_1=-4[/tex]
2. [tex]-2x+8y=5[/tex]
Adding [tex]2x[/tex] both sides.
[tex]-2x+8y+2x=2x+5[/tex]
[tex]8y=2x+5[/tex]
Dividing both sides by 8.
[tex]\frac{8y}{8}=\frac{2x+5}{8}[/tex]
[tex]y=\frac{2x+5}{8}[/tex]
Splitting denominators.
[tex]y=\frac{2x}{8}+\frac{5}{8}[/tex]
Simplifying fraction.
[tex]y=\frac{1}{4}x+\frac{5}{8}[/tex]
So, for the line the slope is.
[tex]m_2=\frac{1}{4}[/tex]
A) Checking for parallel.
For parallel lines the slopes of the line are equal.
Since [tex]m_1\neq m_2[/tex]
So, lines are not parallel.
B) Checking for perpendicular.
For perpendicular line the slopes of the line are related as:
[tex]m_1\times m_2=-1[/tex]
Finding the product of the slopes to check weather it equals -1.
[tex]-4\times\frac{1}{4}[/tex]
⇒ [tex]-1[/tex]
The condition for perpendicular lines is satisfied as the product of the slopes =-1
Hence, the lines are perpendicular to each other.
