Answer:
[tex]y= \frac{-4}{3}x +2[/tex]
Step-by-step explanation:
Given
[tex]AB = (6,6)[/tex]
perpendicular to
[tex]y = \frac{3}{4}x - 11[/tex]
CD parallel to AB
CD passes through (-6,10)
Required
Determine the slope-intercept form of line CD
First, we need to determine the slope of AB
For [tex]y = \frac{3}{4}x - 11[/tex]
Slope, [tex]m_1 = \frac{3}{4}[/tex]
Represent slope of AB with m2
Since both are perpendicular:
[tex]m_2 = -1/m_1[/tex]
[tex]m_2 = -1/\frac{3}{4}[/tex]
[tex]m_2 = -1 * \frac{4}{3}[/tex]
[tex]m_2 = \frac{-4}{3}[/tex]
To determine the equation of CD, we need to determine its slope:
Since CD is parallel to AB, then
[tex]m = m_2 = \frac{-4}{3}[/tex]
The slope intercept form of CD is as follows;
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
[tex](x_1,y_1) = (-6,10)[/tex]
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - 10 = \frac{-4}{3}(x - (-6))[/tex]
[tex]y - 10 = \frac{-4}{3}(x +6)[/tex]
Open Bracket
[tex]y - 10 = \frac{-4}{3}x +\frac{-4}{3} * 6[/tex]
[tex]y - 10 = \frac{-4}{3}x -4 * 2[/tex]
[tex]y - 10 = \frac{-4}{3}x -8[/tex]
Add 10 to both sides
[tex]y - 10 + 10= \frac{-4}{3}x -8 + 10[/tex]
[tex]y= \frac{-4}{3}x +2[/tex]
