What is the equation of the line passing through (180,3), (2,68)?

1 Answer
Jul 13, 2016

The line is y = -65/178 x + 6117/89

Explanation:

The equation for a line takes the form:
y = mx + b

Where m is the slope, and b is the y-intercept. All lines (except vertical lines) are described by equations in this form.

To calculate slope, we use the tried-and-true "rise over run" relationship:
m = (rise)/(run) = (y_2 - y_1)/(x_2 - x_1)

So for our line we have:
m = (3 - 68)/(180 - 2)= -65/178

You'll note here that the order of the x and y didn't matter. If we reversed it we'd end up with:
m = (68-3)/(2-180) = -65/178

So since we know the slope, all we need to do is plug in the known (x,y) pair from one of our given points and compute b:
y = -65/178 x + b
68 = -65/178 * 2 + b
68 = -130/178 + b
b = 6117/89

Combining all our results gives us our line:
y = -65/178 x + 6117/89

You can test that this result is correct by plugging in x = 180 and observing that the result is y = 3.