# Find the equation of the line with a gradient of -1/2 that passes through (4,9) Use algebraic methods ?

##### 1 Answer
Mar 6, 2017

$y = - \frac{1}{2} x + 11$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{point-slope form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the gradient and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

$\text{here "m=-1/2" and } \left({x}_{1} , {y}_{1}\right) = \left(4 , 9\right)$

Substitute these values into the equation.

$\Rightarrow y - 9 = - \frac{1}{2} \left(x - 4\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

distributing the bracket and simplifying gives an alternative version of the equation.

$y - 9 = - \frac{1}{2} x + 2$

$\Rightarrow y = - \frac{1}{2} x + 2 + 9$

$\Rightarrow y = - \frac{1}{2} x + 11 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$