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Write the point slope form of an equation of the line through the points (-7,7) and (4,1)

A) y-7=-6/11(x+7)
B) y-4=-6/11(x-1)
C) y+1=-6/11(x+4)
D) y+7=-6/11(x-7)

Respuesta :

  • (-7,7)
  • (4,1)

Slope:-

  • m=1-7/4+7
  • m=-6/11

Equation in point slope form

  • y-7=-6/11(x+7)

Option A

semsee45

Answer:

[tex]\textsf{A)} \quad y-7=-\dfrac{6}{11}(x+7)[/tex]

Step-by-step explanation:

Step 1:  Find the slope

Define the points:

[tex]\textsf{let}\:(x_1,y_1)=(-7,7)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(4,1)[/tex]

Use the slope formula to find the slope:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-7}{4-(-7)}=-\dfrac{6}{11}[/tex]

Step 2:  Find the equation

Use the found slope from step 1 together with one of the given points in the point-slope form of a linear equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-7=-\dfrac{6}{11}(x-(-7))[/tex]

[tex]\implies y-7=-\dfrac{6}{11}(x+7)[/tex]

Conclusion

Therefore, the equation of the line that passes through the points (-7, 7) and (4, 1) is:

[tex]y-7=-\dfrac{6}{11}(x+7)[/tex]

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