Question

Passing through the pair of points. Write the equation in the form Ax +By = C.

(2,5), (-2,-2)
The equation of the line in the form Ax +By = C is
(Simplify your answer. Use integers or fractions for any numbers in the equation.)

Answer 1

7x - 4y = - 6

Explanation:

Obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2,5) and (x₂, y₂ ) = (- 2, - 2)

m =
`(-2-5)/(-2-2)` =
`(-7)/(-4)` =
`(7)/(4)`, thus

y =
`(7)/(4)` x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 5), then

5 =
`(7)/(2)` + c ⇒ c =
`(3)/(2)`

y =
`(7)/(4)` x +
`(3)/(2)` ← in point- slope form

Multiply through by 4

4y = 7x + 6 ( subtract 4y from both sides )

0 = 7x - 4y + 6 ( subtract 6 from both sides )

- 6 = 7x - 4y, that is

7x - 4y = - 6 ← in standard form