since the slope of this line is -1/4, the slope of the perpendicular line would be 4.
Answer:
the slope of the line that is perpendicular to the line shown is 4
Step-by-step explanation:
Hello
Step 1
find the slope of the line shown using
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\where\\(x_{1},y_{1}) and (x_{2},y_{2}) are\ the\ coordinates\ of\ two\ known\ points\\[/tex]
Let
P1(0,2)
P2(4,1)
replacing
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\m=\frac{1-2}{4-0}\\m=\frac{-1}{4}\\ m=-\frac{1}{4}[/tex]
[tex]m_{1}=-\frac{1}{4}[/tex]
Step 2
two lines are perpendicular when
[tex]m_{1} *m_{2}=-1\\ m_{1} =-\frac{1}{4} \\solve\ for\ m_{2}\\m_{1} * m_{2}=-1\\m_{2}=-\frac{1}{m_{1} }\\replace\\m_{2}=-\frac{1}{-\frac{1}{4} } \\m_{2}=\frac{4}{1} \\m_{2}=4[/tex]
the slope of the line that is perpendicular to the line shown is 4
Have a good day
