What is the slope of the line -2x-5y=11?

May 26, 2017

See a solution process below:

Explanation:

We can transform this line to the Standard Form for Linear Equations. 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

To transform this equation we need to multiply each side of the equation by $\textcolor{red}{- 1}$ to ensure the coefficient for $x$ is positive while keeping the equation balanced:

$\textcolor{red}{- 1} \left(- 2 x - 5 y\right) = \textcolor{red}{- 1} \times 11$

$\left(\textcolor{red}{- 1} \times - 2 x\right) + \left(\textcolor{red}{- 1} \times - 5 y\right) = - 11$

$\textcolor{red}{2} x + \textcolor{b l u e}{5} y = \textcolor{g r e e n}{- 11}$

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

Substituting the $x$ and $y$ coefficients gives:

$m = - \frac{\textcolor{red}{2}}{\textcolor{b l u e}{5}}$

May 26, 2017

The slope is $- \frac{2}{5}$.

Explanation:

Find the slope:

$- 2 x - 5 y = 11$

Solve for $y$, which will give you the slope intercept form of a linear equation: $y = m x + b$, where $m$ is the slope and $b$ is the y-intercept.

Add $2 x$ to both sides of the equation.

$- \textcolor{red}{\cancel{\textcolor{b l a c k}{2 x}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{2 x}}} - 5 y = 2 x + 11$

Simplify.

$- 5 y = 2 x + 11$

Divide both sides by $- 5$.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} y}{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}}} = - \frac{2}{5} x - \frac{11}{5}$

Slope intercept form.

$y = - \frac{2}{5} x - 11$

The slope is $- \frac{2}{5}$