How do you write the slope intercept form of the line 13x-11y=-12?

May 8, 2018

$y = \frac{13}{11} x + \frac{12}{11}$

Explanation:

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

•color(white)(x)y=mx+b

$\text{rearrange "13x-11y=-12" into this form}$

$\text{subtract "13x" from both sides}$

$\cancel{13 x} \cancel{- 13 x} - 11 y = - 13 x - 12$

$\Rightarrow - 11 y = - 13 x - 12$

$\text{multiply through by } - 1$

$11 y = 13 x + 12$

$\text{divide all terms by 11}$

$\Rightarrow y = \frac{13}{11} x + \frac{12}{11} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

May 8, 2018

$y = \frac{13}{11} x + \frac{12}{11}$

Explanation:

The first step is to re-arrange the equation such that $y$ and its coefficients are alone:

$\cancel{13 x} - 11 y \textcolor{red}{\cancel{- 13 x}} = - 12 \textcolor{red}{- 13 x}$

$- 11 y = - 13 x - 12$

Next, divide through by $y$'s coefficient, and you will have slope-intercept form:

$\frac{\cancel{- 11} y}{\textcolor{red}{\cancel{- 11}}} = \frac{\cancel{-} 13 x}{\textcolor{red}{\cancel{-} 11}} + \frac{\cancel{-} 12}{\textcolor{red}{\cancel{-} 11}}$

$\textcolor{g r e e n}{y = \frac{13}{11} x + \frac{12}{11}}$