Answer :
Answer:
The lines are perpendicular.
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\k\ \parallel\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
[tex]\text{We have}\\\\y=-8x-\dfrac{5}{4}\to m_1=-8\\\\y=\dfrac{1}{8}x+\dfrac{4}{5}\to m_2=\dfrac{1}{8}\\\\m_1\neq m_2-\text{given lines are not parallel}\\\\m_1m_2=-8\left(\dfrac{1}{8}\right)=-1-\text{given lines are perpendicular}[/tex]
Answer:
[tex]y= -8x - \frac{5}{4}[/tex]
[tex]y= \frac{1}{8}x + \frac{4}{5}[/tex]
↓
The lines are perpendicular
Step-by-step explanation:
If we have two lines of equations:
[tex]y = nx + v[/tex] (1)
[tex]y = mx + b[/tex] (2)
Where n is the slope of the line (1) and m is the slope of the line (2)
Then by definition it is fulfilled that if [tex]n = -\frac{1}{m}[/tex] means that the lines (1) and (2) are perpendicular
In this case the lines are:
[tex]y= -8x - \frac{5}{4}[/tex] (1)
[tex]y= \frac{1}{8}x + \frac{4}{5}[/tex] (2)
Observe that: [tex]n=-8[/tex] and [tex]m=\frac{1}{8}[/tex]
Then it is fulfilled that [tex]n = -\frac{1}{m}[/tex] because:
[tex]n =-\frac{1}{\frac{1}{8}}[/tex]
[tex]n = -8[/tex]
Therefore the lines are perpendicular