We will graph this equation by finding and plotting its intercepts, then connecting them with a line. To find the $x$- and $y$-intercepts, we will need to substitute $0$ for one variable, solve, then repeat for the other variable.
### Finding the $x$-intercept

Think of the point where the graph of an equation crosses the $x$-axis. The $y$-value of that coordinate pair is equal to $0,$ and the $x$-value is the $x$-intercept. To find the $x$-intercept of the given equation, we should substitute $0$ for $y$ and solve for $x.$
$9x+5y=45$

$9x+5⋅0=45$

$9x=45$

$x=5$

An $x$-intercept of $5$ means that the graph passes through the $x$-axis at the point $(5,0).$ ### Finding the $y$-intercept

Let's use the same concept to find the $y$-intercept. Consider the point where the graph of the equation crosses the $y$-axis. The $x$-value of the coordinate pair at the $y$-intercept is $0.$ Therefore, substituting $0$ for $x$ will give us the $y$-intercept.
$9x+5y=45$

$9⋅0+5y=45$

$5y=45$

$y=9$

A $y$-intercept of $9$ means that the graph passes through the $y$-axis at the point $(0,9).$ ### Graphing the equation

We can now graph the equation by plotting the intercepts and connecting them with a line.

Let's start by identifying the .
### Finding the $x$-intercept

To find the $x$-intercept we'll substitute $0$ for $y$ and then solve for $x.$
$-2x+6.4y=16$

$-2x+6.4⋅0=16$

$-2x=16$

$x=-8$

An $x$-intercept of $-8$ means that the graph passes through the $x$-axis at the point $(-8,0).$ ### Finding the $y$-intercept

To find the $y$-intercept we do the opposite, substituting $x$ for $0.$
$-2x+6.4y=16$

$-2⋅0+6.4y=18$

$6.4y=16$

$y=2.416 $

$y=2.5$

A $y$-intercept of $2.5$ means that the graph passes through the $y$-axis at the point $(0,2.5).$ ### Graphing the equation

We can now graph the equation by plotting the intercepts and connecting them with a line.

One again, we start with the intercepts.
### Finding the $x$-intercept

Here, $y$ is substituted with $0$ and then solve the equation for $x.$
$8x−2y=-8$

$8x+2⋅0=-8$

$8x=-8$

$x=-1$

The $x$-intercept is $(-1,0).$ ### Finding the $y$-intercept

For the $y$-intercept we'll substitute $x$ with $0$ instead.
$8x−2y=-8$

$8⋅0−2y=-8$

$-2y=-8$

$y=4$

The $y$-intercept is $(0,4).$ ### Graphing the equation

We can now graph the equation by plotting the intercepts and connecting them with a line.