What are the intercepts of -6y-2x=5?

Dec 15, 2015

$- 2.5$ or $- \frac{5}{2}$

Explanation:

Solve the equation for y:
$- 6 y - 2 x = 5$
$- 6 y = 5 - 2 x$
$y = \left(\frac{5 - 2 x}{-} 6\right)$
Set the equation equal to zero in order to find the y values that are 0 which are the intercepts
$0 = \left(\frac{5 - 2 x}{-} 6\right)$
In order to get a fraction equal to 0, only the numerator needs to equal 0 so we can ignore the denominator
$0 = - 5 - 2 x$
$5 = - 2 x$
$\frac{5}{-} 2 = x$
Intercept at $\left(- \frac{5}{2} , 0\right)$

Dec 16, 2015

Finding the X-intercept:

Plug $0$ in for $y$.

What this does, in effect, is causes the $- 6 y$ term to disappear.

$\textcolor{red}{\cancel{\textcolor{b l a c k}{- 6 y}}} - 2 x = 5$

$- 2 x = 5$

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

Thus, if $x = - \frac{5}{2}$ and $y = 0$, the point of the $x$-intercept is $\left(- \frac{5}{2} , 0\right)$.

Finding the Y-intercept:

Similar to the previous example, plug in $0$ for $x$. An easy way to think about this is just covering up $- 2 x$ with your finger.

$- 6 y \textcolor{red}{\cancel{\textcolor{b l a c k}{- 2 x}}} = 5$

$y = - \frac{5}{6}$

Which gives us a $y$-intercept of $\left(0 , - \frac{5}{6}\right)$.

The point where the line crosses the $x$-axis (the $x$-intercept) is $\left(- 2.5 , 0\right)$, which equals $\left(- \frac{5}{2} , 0\right)$.
The $y$-intercept on the graph is $\left(0 , - 0.833\right)$, which is equivalent to $\left(0 , - \frac{5}{6}\right)$.