Lines B and C are perpendicular ⇒ answer C
Step-by-step explanation:
The product of the slopes of the perpendicular line is -1
The slopes of the parallel lines are equal
The slopes of two lines are [tex]m_{1}[/tex] and [tex]m_{2}[/tex]
1. If [tex]m_{1}[/tex] × [tex]m_{2}[/tex] = -1, then the two lines are perpendicular
2. If [tex]m_{1}[/tex] = [tex]m_{2}[/tex] , the the two lines are parallel
The equation of a line in slope-intercept form is y = m x + c, where m is
the slope of the line
Line A: y = [tex]\frac{1}{2}[/tex] x + 2
The slope of the line is [tex]m_{A}[/tex] = [tex]\frac{1}{2}[/tex]
Line B: y = [tex]-\frac{1}{2}[/tex] x + 7
The slope of the line is [tex]m_{B}[/tex] = [tex]-\frac{1}{2}[/tex]
Line C: y = 2 x + 4
The slope of the line is [tex]m_{C}[/tex] = 2
Line D: [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{4}[/tex]
The slope of the line is [tex]m_{D}[/tex] = [tex]\frac{1}{2}[/tex]
∵ [tex]m_{B}[/tex] = [tex]-\frac{1}{2}[/tex]
∵ [tex]m_{C}[/tex] = 2
∵ [tex]-\frac{1}{2}[/tex] × 2 = -1
∴ Line B and Line C are perpendicular because the product of their
slopes is -1
Lines B and C are perpendicular
Learn more:
You can learn more about slope in brainly.com/question/4152194
#LearnwithBrainly
