# How do you write the equation of the line containing the point (4, 1) with the slope m = -1/2?

Jun 3, 2017

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

#### Explanation:

Use the point slope formula: $y - {y}_{1} = m \left(x - {x}_{1}\right)$ where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ is a point on the graph.

We are given $m$, the slope, to be $- \frac{1}{2}$ and a point $\left(4 , 1\right)$ which can be referred to as $\left({x}_{1} , {y}_{1}\right)$

Plugging this information into the point-slope formula we get:

$y - 1 = - \frac{1}{2} \left(x - 4\right)$

We can write the equation above in $y = m x + b$ form if desired:

$y - 1 = - \frac{1}{2} x + \frac{4}{2}$

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

$y \cancel{- 1 + 1} = - \frac{1}{2} x + 2 + 1$ <-- (Add $1$ to both sides)

$y = - \frac{1}{2} x + 3$ <-- (Simplify and this is the final answer)

graph{-1/2x+3 [-7.46, 12.54, -1.72, 8.28]}