Answer:[tex]y\text{ = }\frac{-5}{4}x\text{ - 3}[/tex]Explanations:
The equation of a line passing through the points (x₁, y₁) and (x₂, y₂) is given as:
y - y₁ = m (x - x₁)
Where m is the slope of the line given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
For the given points (-4, 2) and (4, -8)
x₁ = -4, y₁ = 2, x₂ = 4, y₂ = -8
Find the slope, m
m = (-8 -2) / (4 - (-4))
m = -10 / 8
m = -5 / 4
Substituting the values of m, x₁, and y₁ into the equation y - y₁ = m (x - x₁):
[tex]\begin{gathered} y\text{ - 2 = }\frac{-5}{4}(x\text{ - (-4))} \\ y\text{ - 2 = }\frac{-5}{4}(x\text{ + 4)} \\ y\text{ - 2 = }\frac{-5}{4}x\text{ - 5} \end{gathered}[/tex]
Simplify the equuation above to the form y = mx + b
[tex]\begin{gathered} y\text{ = }\frac{-5}{4}x\text{ - 5 + 2} \\ y\text{ = }\frac{-5}{4}x\text{ - 3} \end{gathered}[/tex]
