Question

How do you write an equation of a line with point (5,-3), (2,5)?

Answer 1

`(8)/(-3)` = `m`
`y = 8/-3x + 49/-3`

Explanation:

The goal of this question is to find the slope from two ordered pairs (two points on the graph). To do this, use this equation:

`(Y_2 - Y_1)/(X_2 - X_1)` =`m`, the slope

Next, let's label our ordered pairs, or points, as `X_1`, `Y_1`, `X_2`, and `Y_2`. List your ordered pairs. Recall that an ordered pair is in the form `(x, y)`.

`(5, -3)` `(X_1, Y_1)`
`(2, 5)` `(X_2, Y_2)`

Now, plug this information into your equation:

`(Y_2 - Y_1)/(X_2 - X_1)` =`m`

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

Two negatives make a positive, so:
`(5 + 3)/(2 - 5)` = `m`

Simplify.

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

The slope, `m`, is `(8, -3)`. If you want to continue to find the whole line in the form of `y = mx + b`, use the point-slope formula as shown below. Recall that `m` is the slope and the ordered pair you'll be using is the one you labeled as `(X_1, Y_1)`.

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

Plug in your information:
`(y - -3) = (8/-3)(x - 5)`

Distribute:
`(y + 3) = (8/-3x) + (-40/3)`

Subtract 3 from both sides to isolate for y:
`y = (8/-3x) + (49/-3)`

Remove parentheses:

`y = 8/-3x + 49/-3`