Answer:
[tex]y =-\frac{3}{2}x + 6[/tex]
Step-by-step explanation:
Given
[tex]y = []x + 6[/tex] --- equation 1
[tex]y = \frac{2}{3}x + 10[/tex] --- equation 2
Required
Fill in the blank
A linear equation is represented as:
[tex]y = mx + b[/tex]
Where m represents the slope
If (1) and (2) are perpendicular, then:
[tex]m_1 = -\frac{1}{m_2}[/tex]
In [tex]y = \frac{2}{3}x + 10[/tex] --- equation 2
[tex]m_2 = \frac{2}{3}[/tex]
So, we have:
[tex]m_1 = -\frac{1}{m_2}[/tex]
[tex]m_1 = -\frac{1}{2/3}[/tex]
[tex]m_1 = -\frac{3}{2}[/tex]
Hence, the complete equation is:
[tex]y =-\frac{3}{2}x + 6[/tex]
