Answer:
[tex]y +5 = -\frac{2}{3}(x - 4)[/tex]
Step-by-step explanation:
Given
[tex]y = -\frac{2}{3}x + 8[/tex]
Point (4,-5)
Required
Determine the line equation
From the question, we understand that the line is parallel to [tex]y = -\frac{2}{3}x + 8[/tex]
This implies that they have the same slope, m
A linear equation is:
[tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison: [tex]y = mx + b[/tex] and [tex]y = -\frac{2}{3}x + 8[/tex]
[tex]m = -\frac{2}{3}[/tex]
Next, we determine the line equation using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex](x_1,y_1) = (4,-5)[/tex] and [tex]m = -\frac{2}{3}[/tex]
[tex]y - (-5) = -\frac{2}{3}(x - 4)[/tex]
[tex]y +5 = -\frac{2}{3}(x - 4)[/tex]
Hence,
Option C is correct
