# How do you find the slope and y intercept for 2x-7y=44?

Jun 2, 2018

See a solution process below:

#### Explanation:

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

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: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

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

$\textcolor{red}{2} x - \textcolor{b l u e}{7} y = \textcolor{g r e e n}{44}$

Or

$\textcolor{red}{2} x + \left(\textcolor{b l u e}{- 7} y\right) = \textcolor{g r e e n}{44}$

Therefore:

• The slope of the line is: $m = \frac{- \textcolor{red}{2}}{\textcolor{b l u e}{- 7}} = \frac{2}{7}$

• The $y$-intercept is: $\frac{\textcolor{g r e e n}{C}}{\textcolor{b l u e}{B}} = \frac{44}{-} 7 = - \frac{44}{7}$ or $\left(0 , - \frac{44}{7}\right)$