# How do you find the slope and y intercept to sketch 7x+6y=30?

Mar 4, 2018

See a solution process below:

#### Explanation:

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

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

$\textcolor{red}{7} x + \textcolor{b l u e}{6} y = \textcolor{g r e e n}{30}$

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

Substituting the values from the equation in the problem gives:

$m = - \frac{\textcolor{red}{7}}{\textcolor{b l u e}{6}}$

The $y$-intercept of an equation in standard form is: $\frac{\textcolor{g r e e n}{C}}{\textcolor{b l u e}{B}}$

Substituting the values from the equation in the problem gives:

$\frac{\textcolor{g r e e n}{30}}{\textcolor{b l u e}{6}} = 5$ or $\left(0 , 5\right)$