# How to find the y-intercept given 7x - 14y = 35?

Mar 11, 2018

See a solution process below:

#### Explanation:

First, divide each side of the equation by $\textcolor{red}{7}$ to reduce the coefficients:

$\frac{7 x - 14 y}{\textcolor{red}{7}} = \frac{35}{\textcolor{red}{7}}$

$\frac{7 x}{\textcolor{red}{7}} - \frac{14 y}{\textcolor{red}{7}} = \frac{35}{\textcolor{red}{7}}$

$1 x - 2 y = 5$

This equation is now in Standard Linear Form. The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

$\textcolor{red}{1} x - \textcolor{b l u e}{2} y = \textcolor{g r e e n}{5}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

The slope of an equation in standard form is: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

Substituting gives:

$m = - \frac{\textcolor{red}{1}}{\textcolor{b l u e}{- 2}} = \frac{1}{2}$