# What is the equation of the line that has a slope of m=3/4 and goes through (5,2)?

Mar 16, 2017

$y = \frac{3}{4} x - \frac{7}{4}$

#### 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 slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

$\text{here "m=3/4" and } \left({x}_{1} , {y}_{1}\right) = \left(5 , 2\right)$

$\Rightarrow y - 2 = \frac{3}{4} \left(x - 5\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

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

$y - 2 = \frac{3}{4} x - \frac{15}{4}$

$\Rightarrow y = \frac{3}{4} x - \frac{15}{4} + 2$

$\Rightarrow y = \frac{3}{4} x - \frac{7}{4} \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$