# How do you write the point-slope form of an equation of the line that passes through the given point (6,2), m=1/2?

Jul 16, 2016

$y = \frac{1}{2} x - 1$

#### Explanation:

There is a nifty formula for the equation of a line which applies in just such a case where we are given the slope and one point.

Using this formula requires only ONE step with substitution and some easy simplifying. Works like a dream...

$y - {y}_{1} = m \left(x - {x}_{1}\right) \text{ m = slope and "(x_1,y_1)" is a point}$

Substitute the given values and simplify

$y - 2 = \frac{1}{2} \left(x - 6\right)$

$y = \frac{1}{2} x - 3 + 2$

$y = \frac{1}{2} x - 1$