To determine the $x -$ and $y -$ intercepts of a line, we need to substitute $0$ for one variable, solve, then repeat for the other variable.

Think of the point where the graph of an equation crosses the

x -

axis. The

y -

value of that

(x, y)

0,

and the

x -

value is the

x -

intercept. To find the

x -

intercept of the equation we should substitute

0

for

y

and solve for

x .

- 3 x + 3 y = 7

$y = 0$

- 3 x + 3 (0) = 7

Zero Property of Multiplication

- 3 x = 7

$LHS / - 3 = RHS / - 3$

x = \frac{7}{- 3}

Put minus sign in front of fraction

x = - \frac{7}{3}

An

x -

intercept of

- \frac{7}{3}

means that the graph passes through the

x -

axis at the point

(- \frac{7}{3}, 0) .

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.

- 3 x + 3 y = 7

$x = 0$

- 3 (0) + 3 y = 7

Zero Property of Multiplication

3 y = 7

$LHS / 3 = RHS / 3$

y = \frac{7}{3}

A

y -

intercept of

\frac{7}{3}

means that the graph passes through the

y -

axis at the point

(0, \frac{7}{3}) .

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