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Complete the equation of the line through (-9,7)and(-6-3)use exact numbers

Sagot :

Mathkot

Answer:

[tex]\boxed{y = -\dfrac{10}{3}x - 23}[/tex]

Step-by-step explanation:

Equation of a straight line: y = kx + b

Points: (-9,7) and (-6,-3)

Сompose the system of equations:

[tex]\displaystyle \left \{ {{7=-9k + b} \atop {-3=-6k + b}} \right[/tex] [tex]\displaystyle \left \{ {{b= 7 + 9k} \atop {b=6k - 3}} \right \Longrightarrow 7 + 9k = 6k - 3[/tex]

[tex]7 + 9k = 6k - 3[/tex]

[tex]3k = -10|:3[/tex]

[tex]k = -\dfrac{10}{3}[/tex]

[tex]b = 6k - 3= 6 \cdot \dfrac{-10}{3} - 3 = 2 \cdot (-10) - 3 = -20 - 3 = -23[/tex]

[tex]y = -\dfrac{10}{3}x - 23[/tex]

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