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 .

- 5 x + 3 y = - 7.5

$y = 0$

- 5 x + 3 (0) = - 7.5

▼

Solve for

x

Zero Property of Multiplication

- 5 x = - 7.5

$LHS / - 5 = RHS / - 5$

x = \frac{- 7 . 5}{- 5}

$\frac{- a}{- b} = \frac{a}{b}$

x = \frac{7 . 5}{5}

Calculate quotient

x = 1.5

An

x -

intercept of

1.5

means that the graph passes through the

x -

axis at the point

(1.5, 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.

- 5 x + 3 y = - 7.5

{{ 'ml-heading-exercise' | message }} {{ exercise.name }} {{ 'ml-label-page' | message }} {{ exercise.page }}