# How do you write an equation in slope intercept form for the line through the given point (5, -2) and (-16, 4)?

Mar 25, 2015

The slope of your line is: $m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ and represents the inclination of your line (change in $y$ for a change in $x$).

In your case you have: $m = \frac{4 - \left(- 2\right)}{- 16 - 5} = \frac{6}{-} 21 = - \frac{2}{7}$

you can now insert this slope into the relationship:

$y - {y}_{0} = m \left(x - {x}_{0}\right)$ that gives the equation of your line using, for example, the coordinates of your first point as:

$y - \left(- 2\right) = - \frac{2}{7} \left(x - 5\right)$

giving: $y = \left(- \frac{2}{7}\right) x - \left(\frac{4}{7}\right)$

So you have a line of slope $m = - \frac{2}{7}$ and intercept at $y = - \frac{4}{7}$