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 - 5 y = - 20

$y = 0$

3 x - 5 (0) = - 20

Zero Property of Multiplication

3 x = - 20

$LHS / 3 = RHS / 3$

x = \frac{- 2 0}{3}

Put minus sign in front of fraction

x = - \frac{2 0}{3}

An

x -

intercept of

- \frac{2 0}{3}

means that the graph passes through the

x -

axis at the point

(- \frac{2 0}{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 - 5 y = - 20

$x = 0$

3 (0) - 5 y = - 20

Zero Property of Multiplication

- 5 y = - 20

$LHS / (- 5) = RHS / (- 5)$

y = 4

A

y -

intercept of

4

means that the graph passes through the

y -

axis at the point

(0, 4) .

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