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What is an equation of the line that passes through the points (-6, -4) and (3, 8)

Sagot :

Answer:

y = [tex]\frac{4}{3}[/tex] x + 4

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 ) = (- 6, - 4) and (x₂, y₂ ) = (3, 8)

m = [tex]\frac{8-(-4)}{3-(-6)}[/tex] = [tex]\frac{8+4}{3+6}[/tex] = [tex]\frac{12}{9}[/tex] = [tex]\frac{4}{3}[/tex] , then

y = [tex]\frac{4}{3}[/tex] x + c ← is the partial equation

To find substitute either of the 2 points into the partial equation

Using (3, 8 ) , then

8 = 4 + c ⇒ c = 8 - 4 = 4

y = [tex]\frac{4}{3}[/tex] x + 4 ← equation of line

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