To determine the relationship between the lines [tex]\( y = 4x + 17 \)[/tex] and [tex]\( y = -0.25x + 13 \)[/tex], we compare their slopes:
For the first line, [tex]\( y = 4x + 17 \)[/tex], the slope is [tex]\( 4 \)[/tex].
For the second line, [tex]\( y = -0.25x + 13 \)[/tex], the slope is [tex]\( -0.25 \)[/tex].
The relationship between two lines depends on their slopes:
Now, calculating the product of the slopes:
[tex]$\begin{align*}\text{Product of slopes} &= \text{Slope of first line} \times \text{Slope of second line}\\[1em]&= 4 \times (-0.25)\\[1em]&= \boxed{-1.0}\end{align*}[/tex]
Since the product of the slopes is [tex]\( -1 \)[/tex], the lines [tex]\( y = 4x + 17 \)[/tex] and [tex]\( y = -0.25x + 13 \)[/tex] are perpendicular.
