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Answer:
[tex]{\huge\color{yellow}{\boxed{\fcolorbox{yellow}{purple}{Pa Brainliest}}}}[/tex]
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1. Calculate the slope (m):
The slope of a line passing through two points:
[tex] \((x_1, y_1)\) and \((x_2, y_2)\) is given by[/tex]
[tex] \[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
[tex]Plugging in the given points \((8, 3)\) and \((-4, 9)\):
\[
m = \frac{9 - 3}{-4 - 8} = \frac{6}{-12} = -\frac{1}{2}
\][/tex]
2. Use the point-slope form of the equation:
The point-slope form of a line's equation is:
[tex] \[
y - y_1 = m(x - x_1)
\]
[/tex]
[tex]Using the point \((8, 3)\) and the slope [/tex]
[tex]\(m = -\frac{1}{2}\):[/tex]
[tex]
\[
y - 3 = -\frac{1}{2}(x - 8)
\][/tex]
3. Simplify to the slope-intercept form
[tex](y = mx + b)[/tex]
Distribute the slope and simplify:
[tex]\[
y - 3 = -\frac{1}{2}x + 4
\][/tex]
Add 3 to both sides to solve for
[tex]\(y\):
\[
y = -\frac{1}{2}x + 4 + 3
\]
\[
y = -\frac{1}{2}x + 7
\][/tex]
So the equation of the line is
[tex]\(y = -\frac{1}{2}x + 7\),[/tex]
which corresponds to option B:
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[tex]B. \(Y = -\frac{1}{2}x + 7\)[/tex]
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