# How do you find the equation of a line passing through (4, 1) with the slope m = -1/2?

Apr 29, 2018

See below:

#### Explanation:

Point $\left({x}_{1} , {y}_{1}\right) = \left(4 , 1\right)$

Slope ($m$) $= - \frac{1}{2}$

Let the equation of the line be

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

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

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

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

which is the required equation of the line.

Apr 29, 2018

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

#### Explanation:

Slope-intercept form of a line: $y = m x + b$, with $m$ as the slope and $b$ as the y-intercept

We know that the slope is $- \frac{1}{2}$, so we can put that in for $m$:

$y = - \frac{1}{2} x + b \rightarrow$ To find the y-intercept, plug in the point $\left(4 , 1\right)$ and solve

$1 = - \frac{1}{2} \cdot 4 + b$

$1 = - 2 + b$

$b = 3$

The equation in slope-intercept form is $y = - \frac{1}{2} x + 3$