Question

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)

Answer 1

• (-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

Answer 2

`\textsf{A)} \quad y-7=-(6)/(11)(x+7)`

Explanation:

Step 1: Find the slope

Define the points:

`\textsf{let}\:(x_1,y_1)=(-7,7)`

`\textsf{let}\:(x_2,y_2)=(4,1)`

Use the slope formula to find the slope:

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

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:

`\implies y-y_1=m(x-x_1)`

`\implies y-7=-(6)/(11)(x-(-7))`

`\implies y-7=-(6)/(11)(x+7)`

Conclusion

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

`y-7=-(6)/(11)(x+7)`