# How do you write an equation in standard form for a line with a slope of 1/4 and goes through point (4, 0)?

Apr 20, 2018

$x - 4 y = 4$

#### Explanation:

$\text{the equation of a line in "color(blue)"standard form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{A x + B y = C} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where A is a positive integer and B, C are integers}$

$\text{to begin express the equation in "color(blue)"point-slope form}$

•color(white)(x)y-y_1=m(x-x_1)

$\text{where m is the slope and "(x_1,y_1)" a point on the line}$

$\text{here "m=1/4" and } \left({x}_{1} , {y}_{1}\right) = \left(4 , 0\right)$

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

$\Rightarrow y = \frac{1}{4} x - 1$

$\text{multiply all terms by 4}$

$\Rightarrow 4 y = x - 4$

$\Rightarrow x - 4 y = 4 \leftarrow \textcolor{red}{\text{in standard form}}$