How do you find the x and y intercepts of 4x=-1/2y-1?

Jul 7, 2017

See a solution process below:

Explanation:

$x$-intercept:

To find the $x$-intercept, substitute $0$ for $y$ and solve for $x$:

$4 x = - \frac{1}{2} y - 1$ becomes:

$4 x = \left(- \frac{1}{2} \times 0\right) - 1$

$4 x = 0 - 1$

$4 x = - 1$

$\frac{4 x}{\textcolor{red}{4}} = - \frac{1}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}} = - \frac{1}{4}$

$x = - \frac{1}{4}$

The $x$-intercept is: $- \frac{1}{4}$ or $\left(- \frac{1}{4} , 0\right)$

$y$-intercept:

To find the $y$-intercept, substitute $0$ for $x$ and solve for $y$:

$4 x = - \frac{1}{2} y - 1$ becomes:

$\left(4 \cdot 0\right) = - \frac{1}{2} y - 1$

$0 = - \frac{1}{2} y - 1$

$0 + \textcolor{red}{1} = - \frac{1}{2} y - 1 + \textcolor{red}{1}$

$1 = - \frac{1}{2} y - 0$

$1 = - \frac{1}{2} y$

$1 \times \textcolor{red}{- 2} = \frac{1}{-} 2 y \times \textcolor{red}{- 2}$

$- 2 = \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}}} y \times \cancel{\textcolor{red}{- 2}}$

$- 2 = y$

$y = - 2$

The $y$-intercept is: $- 2$ or $\left(0 , - 2\right)$