Answer:
[tex]y = \frac{2}{3}x + \frac{7}{3}[/tex]
Step-by-step explanation:
Given
Line A:
[tex]y = -\frac{2}{3}x - 4[/tex]
Line B:
[tex](-2,1)[/tex]
Required
Determine the equation of Line B
First, we need to determine the slope of A using
[tex]y =mx + b[/tex]
Where:
[tex]m = slope[/tex]
By comparison:
[tex]y = -\frac{2}{3}x - 4[/tex]
[tex]m = -\frac{2}{3}[/tex]
Since A and B are perpendicular:
The slope of B (m2) is:
[tex]m_2 = \frac{-1}{m}[/tex]
[tex]m_2 = -1/\frac{-2}{3}[/tex]
[tex]m_2 = -1 * \frac{-3}{2}[/tex]
[tex]m_2 = \frac{3}{2}[/tex]
The equation of B is calculated as thus:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex](x_1,y_1) = (-2,1)[/tex]
[tex]m = \frac{2}{3}[/tex]
So, the equation becomes
[tex]y - 1 = \frac{2}{3}(x - (-2))[/tex]
[tex]y - 1 = \frac{2}{3}(x + 2)[/tex]
Open bracket
[tex]y - 1 = \frac{2}{3}x + \frac{4}{3}[/tex]
Make y the subject
[tex]y = \frac{2}{3}x + \frac{4}{3} + 1[/tex]
[tex]y = \frac{2}{3}x + \frac{4 + 3}{3}[/tex]
[tex]y = \frac{2}{3}x + \frac{7}{3}[/tex]
