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

(x, y)

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 .

6 x - 2 y = 18

Substitute

$y = 0$

6 x - 2 (0) = 18

ZeroPropMult

Zero Property of Multiplication

6 x - 0 = 18

SubTerm

Subtract term

6 x = 18

DivEqn

$LHS / 6 = RHS / 6$

x = 3

An $x -$ intercept of $3$ means that the graph passes through the $x -$ axis at the point $(3, 0) .$

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

(x, y)

coordinate pair at the

y -

intercept is

0 .

Therefore, substituting

0

for

x

will give us the

y -

intercept.

6 x - 2 y = 18

Substitute

$x = 0$

6 (0) - 2 y = 18

ZeroPropMult

Zero Property of Multiplication

0 - 2 y = 18

IdPropAdd

Identity Property of Addition

- 2 y = 18

DivEqn

$LHS / - 2 = RHS / - 2$

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.

Finding the x-intercept

Finding the y-intercept

Graphing the Equation

Finding the $x -$ intercept

Finding the $y -$ intercept

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