# What is the equation of the line with slope  m= -1/2  that passes through  (5,3) ?

Mar 24, 2018

The equation of the line is $y = - \frac{1}{2} x + \frac{11}{2}$

#### Explanation:

As you know, equation of a line can be presented by y=mx+c (slope-intercept form). our slope (m)=$- \frac{1}{2}$ so we will have to find c (the y-intercept). The rest is shown above.

$y = 3$ , $x = 5$ and $m = - \frac{1}{2} \rightarrow$ We then substitute what we were given into our equation:

$3 = \left(- \frac{1}{2}\right) \cdot 5 + c \rightarrow$ We work out what we have

$3 = \left(- \frac{5}{2}\right) + c \rightarrow$ Add$\left(- \frac{5}{2}\right)$ to both sides which gives us $c = \frac{11}{2}$, therefore equation of the line is $y = - \frac{1}{2} x + \frac{11}{2}$