Method

Finding the Intercepts of a Graph

The intercepts of a graph share an important feature. For all

x

-intercepts, the

y

-coordinate is

0,

and for all

y

-intercepts, the

x

-coordinate is

0 .

x - int y - int : (x, 0) : (0, y)

This can be used to find the intercepts of a graph when its rule is known. For example, consider the line given by the following equation.

2 x + 5 y = 10

Method

Finding the $x$ -intercept

To find the

x

-intercept,

y = 0

can be substituted into the equation.

2 x + 5 y = 10 \Rightarrow 2 x + 5 \cdot 0 = 10

Next, solve the equation for

x .

2 x + 5 \cdot 0 = 10

2 x = 10

$LHS / 2 = RHS / 2$

x = 5

The

x

-intercept is

(5, 0) .

Method

The

y

-intercept can be found in a similar way. Substitute

x = 0

into the equation and solve for

y .

2 \cdot 0 + 5 x = 10

5 y = 10

$LHS / 2 = RHS / 2$

y = 2

The

y

-intercept is

(0, 2) .