Answer:
[tex]y = -5[/tex]
Step-by-step explanation:
Given
[tex]B = (7,-3)[/tex]
[tex]C = (6,y)[/tex]
[tex]A = (4,-9)[/tex]
Required
The y coordinate of C
Since A, B and C are on the same line, the slope of AB and the slope of AC will be the same.
Slope (m) is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
For AC
[tex]A = (4,-9)[/tex] [tex]C = (6,y)[/tex]
[tex]m = \frac{y - -9}{6 - 4}[/tex]
[tex]m = \frac{y +9}{2}[/tex]
For AB
[tex]A = (4,-9)[/tex] [tex]B = (7,-3)[/tex]
[tex]m = \frac{-3 --9}{7-4}[/tex]
[tex]m = \frac{-3 +9}{3}[/tex]
[tex]m = \frac{6}{3}[/tex]
[tex]m = 2[/tex]
So, we have:
[tex]m = \frac{y +9}{2}[/tex] and [tex]m = 2[/tex]
[tex]m = m[/tex]
[tex]\frac{y +9}{2} = 2[/tex]
Multiply both sides by 2
[tex]y +9 = 4[/tex]
Solve for y
[tex]y = 4-9[/tex]
[tex]y = -5[/tex]
Hence, the y coordinate of C is -5
