Find standard form

Question

(h,k)=(-5,3), (x,y)=(2,9)

Answer 1

To get the standard form of a line wiht two points, you must:

1. Find the slope:
2. (9-3) / (2 - (-5)) = 6/7
3. Use the slope to write the equation in point-slope form
4. y - y₁ = m (x - x₁)
5. Here (x₁,y₁) would be one of the points: we will use (2,9)
6. y - 9 = (6/7) (x - 2)
7. Distribute the slope and solve for y
8. y -9 = (6/7)x - (6/7) *2
9. y = 9 - (12/7) + (6/7)x
10. Move x to the left side of the equation
11. y - (6/7)x = (63/7) - (12/7)
12. y - (6/7)x = 51/7
13. Make sure the coefficient of x is a positive integer
14. -7y + 6x = -51

Thus the final answer is 6x -7y = -51.