Answer:
[tex]y = \frac{4}{3}x - 12[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (3,-8)[/tex]
[tex](x_2,y_2) = (6,-4)[/tex]
Required
Determine the equation
First, we need to determine the slope (m):
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-4 - (-8)}{6 -3}[/tex]
[tex]m = \frac{-4 +8}{3}[/tex]
[tex]m = \frac{4}{3}[/tex]
Next, we determine the line equation using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = \frac{4}{3}[/tex]
[tex](x_1,y_1) = (3,-8)[/tex]
[tex]y - (-8) = \frac{4}{3}(x - 3)[/tex]
[tex]y +8 = \frac{4}{3}(x - 3)[/tex]
[tex]y +8 = \frac{4}{3}x - 4[/tex]
[tex]y = \frac{4}{3}x - 4 - 8[/tex]
[tex]y = \frac{4}{3}x - 12[/tex]
The equation of the line that passes through (3, -8)(6, -4) is y = - 1 / 2 x - 1
The slope intercept equation is as follows:
y = mx + b
where
m = slope
b = y-intercept
Therefore,
The line passes through (3, -8)(6, -4)
m = -4 - 3 / 6 + 8 = -7 / 14 = - 1 / 2
y = - 1 /2 x + b
let's find b using (6, -4)
-4 = - 1 /2 (6) + b
-4 + 3 = b
b = -1
Therefore,
y = - 1 / 2 x - 1
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