what is the slope of a line perpendicular to this line?
what is the slope of a line perpendicular to this line?
Answer
Answer:
B. ( m = 3 )
Explanation:
Step1: Calculate the slope of the given line
Use the slope formula ( m=\frac{y_2 - y_1}{x_2 - x_1} ). Let's take two points on the line, say ((-4,2)) and ((1,0)). Then (m_1=\frac{0 - 2}{1-(-4)}=\frac{-2}{5}) (Wait, no, wait. Wait, looking at the line, if we take ((-2,1)) and ((4,-1)). Then (m_1=\frac{-1 - 1}{4-(-2)}=\frac{-2}{6}=-\frac{1}{3})
Step2: Use the perpendicular - slope relationship
If two lines are perpendicular, the product of their slopes is (- 1), i.e., (m_1\times m_2=-1). Given (m_1 =-\frac{1}{3}), then (-\frac{1}{3}\times m_2=-1). Solving for (m_2), we get (m_2 = 3) (Multiply both sides by (-3): (m_2=(-1)\times(-3)))