Write the equation of the line in standard form

Question

Through (2,-7) and (3,-1)

Answer 1

First, let's find your line's slope. Slope is rise/run, or (change in y) / (change in x):

 

m = (y₂ - y₁) / (x₂ - x₁)

m = (-1 - (-7)) / (3 - 2)

m = 6/1

m = 6

 

 

Now, write your line's equation in point-slope form, using slope m = 6 and point (x₁, y₁) = (2, -7):

 

y - y₁ = m(x - x₁)

y + 7 = 6(x - 2)

 

 

Finally, rearrange that equation into standard form (Ax + By = C) by getting x and y together on one side:

 

y = 6(x - 2) - 7

y = 6x - 12 - 7

-6x + y = -19