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Please find the equation of the line that goes through the point (5,-10) and (2,8)
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y = - 6x + 20

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (5, - 10 ) and (x₂, y₂ ) = (2, 8 )

m = [tex]\frac{8-(-10)}{2-5}[/tex] = [tex]\frac{8+10}{-3}[/tex] = [tex]\frac{18}{-3}[/tex] = - 6 , then

y = - 6x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (2, 8 ) , then

8 = - 12 + c ⇒ c = 8 + 12 = 20

y = - 6x + 20 ← equation of line
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