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

1 Answer
May 31, 2018

(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