Question

What is the equation of the line that passes through (5, -2) and (-3, 4)?

3x - 4y - 7 = 0
-3x + 4y - 7 = 0
3x + 4y - 7 = 0

Answer 1

`\boxed{3x + 4y - 7 = 0}`

.

Explanation:

First step, find the slope of the line

`\boxed{\boxed{m = (y_2 - y_1)/(x_2 - x_1) }}`

Where

• m is a slope.
• 
  `(x_1,~y_1)` and
  `(x_2,~y_2)` are point of the line.

So

`m = (4 - (-2))/(-3 - 5)`

`m = (4 + 2)/(-8)`

`m = (6)/(-8)`

`m = - (3)/(4)`

Next step, find the equation

`\boxed{\boxed{y - y_1 = m(x - x_1)}}`

So

`y - (-2) = -(3)/(4)(x - 5)`

`y + 2 = -(3)/(4)(x - 5)`

`4(y + 2) = -3(x - 5)`

`4y + 8 = -3x + 15`

`3x + 4y + 8 - 15 = 0`

`3x + 4y - 7 = 0`

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Happy to help :)