# How do you graph using the intercepts for -6x+5y=1?

Jun 17, 2018

See below

#### Explanation:

First of all, observe that your equation represents a line, since it can be written as $a x + b y + c = 0$.

This is important, because we know that two points are sufficient to draw a line. And these two points will be the intercepts of the line.

The intercepts are the points in which the line crosses one of the axis. By definition, the axis are defined as the set of points where one coordinate equals zero: the $x$ axis is the set of the points $\left(x , 0\right)$, i.e. the $y$ coordinate is zero, and vice versa the $y$ axis is the set of the points $\left(0 , y\right)$, i.e. the $x$ coordinate is zero.

So, if we set $x = 0$, we will find the $y$ intercept of the line: the equation becomes

$- 6 \left(0\right) + 5 y = 1 \setminus \iff 5 y = 1 \setminus \iff y = \frac{1}{5}$

So, the $y$ intercept is the point $\left(0 , \frac{1}{5}\right)$.

If we set $y = 0$, we will find the $x$ intercept of the line: the equation becomes

$- 6 x + 5 \left(0\right) = 1 \setminus \iff - 6 x = 1 \setminus \iff x = - \frac{1}{6}$

So, the $y$ intercept is the point $\left(- \frac{1}{6} , 0\right)$.

Connect these two points and you have your line!