The value of p is 0.
A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
Given that
Point A(p8,4p+5) is located on a line that connects M(-2,-5) and N(1,-10).
The equation of line that passing through points M and N,
Use the formula of equation of line,
y-y₁ = (y₂-y₁/x₂-x₁)(x-x₁)
y-(-5) = (-10+5/1+2)(x-(-2))
⇒ y+5 = -5/3(x+2)
⇒5x+3y +25 = 0 (1)
Since, line passes through point A(p−8,4p+5), so this point A will satisfy the equation (1)
5(p-8)+3(4p+5)+25 = 0
⇒ 17p = 0
⇒ p = 0
The value of p is 0.
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