Answer:
Step-by-step explanation:
Step 1: Find slope of Linear function A
[tex]slope = \frac{y_2 - y_1}{x_2-x_1} = \frac{-5--1}{-4--2} = \frac{-5 +1}{-4+2} = \frac{-4}{-2} = 2[/tex]
Step 2 : Find slope of B
Since they are perpendicular to each other, product of their slope = -1
That is,
[tex]m_A \times m_B = - 1\\2 \times m_B = -1\\\\slope, m_B = \frac{-1}{2}[/tex]
Given the function passes through (4, -6)
Equation of the linear function :
[tex]x_3 = 4 \ , \ y_3 = -6\\\\(y - y_3) = m_B (x - x_3)\\\\(y - -6) = -\frac{1}{2} (x - 4)\\\\y + 6 = -\frac{1}{2}x + 2\\\\y = -\frac{1}{2}x + 2 - 6 \\\\y = -\frac{1}{2}x -4[/tex]
Part B
Linear Function is parallel to B
Therefore the slope of B and slope of C are the same. And the equation will be of the form :
[tex]y = -\frac{1}{2} x + C[/tex]
