# What is the linear equation 10y=-6x-9 in standard form?

Mar 12, 2015

The equation for a line in standard form, or slope-intercept form, is $y = m x + b$, where $m$ is the slope, and $b$ is the y-intercept.

To convert the equation $10 y = - 6 x - 9$ to standard form, do the following:

1. Divide both sides of the equation by 10:

$\frac{10 y}{10} = - \frac{6 x}{10} - \frac{9}{10}$
$y = - \frac{6 x}{10} - \frac{9}{10}$

2. Reduce $- \frac{6 x}{10}$ to $- \frac{3 x}{5}$, and you will get the equation in standard form:

$y = - \frac{3}{5} x - \frac{9}{10}$.

The slope ($m$) is $- \frac{3}{5}$, and the y-intercept ($b$) is $- \frac{9}{10}$.

Graphically, this is what the function looks like:

Usually, if the question asks where does a line intersect the y-axis or the y-intercept, it is usually written in terms of a point on a graph where x = 0.
In this equation, the point is $\left(0 , - \frac{9}{10}\right)$.