Given:
y = -4x + 1
4y = x + 3
Since the first equation is already in slope-intercept form, let's rewrite the second equation to slope-intercept form.
4y = x + 3
Divide through by 4:
[tex]\begin{gathered} \frac{4y}{4}=\frac{x}{4}+\frac{3}{4} \\ \\ y=\frac{1}{4}x+\frac{3}{4} \end{gathered}[/tex]Parallel lines have similar slope, while the slope of perpendicular lines are negative reciprocals of each other.
Using:
y = mx + b
Where m = slope
Slope of the first line y = -4x + 1 is -4
Slope of the second line: = ¼
[tex]y=\frac{1}{4}x+\frac{3}{4}[/tex]The negative reciprocal of -4 is ¼.
Therefore, the lines are perpendicular to each other since the slope of the second line is the neagtive reciprocal of the first line.
ANSWER:
Perpendicular lines
