The equation that could represent the line containing the perpendicular leg is y = 1/4 x + 2 and this can be determined by using the given data.
Given :
The equation of a line containing one leg of a right triangle is (y = -4x).
The following steps can be used in order to determine the equation that could represent the line containing the perpendicular leg:
Step 1 - If the two lines are perpendicular then the below relation of slopes is followed.
[tex]\rm m_1m_2=-1[/tex]
where [tex]\rm m_1[/tex] is the slope of one line and [tex]\rm m_2[/tex] is the slope of another line.
Step 2 - Now, the slope of the line containing the perpendicular leg is:
[tex]\rm m_2 = \dfrac{1}{4}[/tex]
Step 3 - So, from the given options the line that contains the perpendicular leg is:
y = 1/4 x + 2
Therefore, the correct option is A).
For more information, refer to the link given below:
https://brainly.com/question/2564656
