Find the x and y Intercepts 10x+3y=1

$10 x + 3 y = 1$

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$10 x + 3 (0) = 1$

Solve the equation.

Simplify $10 x + 3 (0)$ .

Multiply $3$ by $0$ .

$10 x + 0 = 1$

Add $10 x$ and $0$ .

$10 x = 1$

Divide each term in $10 x = 1$ by $10$ and simplify.

Divide each term in $10 x = 1$ by $10$ .

$\frac{10 x}{10} = \frac{1}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{1}{10}$

Divide $x$ by $1$ .

$x = \frac{1}{10}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{10}, 0)$

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$10 (0) + 3 y = 1$

Solve the equation.

Simplify $10 (0) + 3 y$ .

Multiply $10$ by $0$ .

$0 + 3 y = 1$

Add $0$ and $3 y$ .

$3 y = 1$

Divide each term in $3 y = 1$ by $3$ and simplify.

Divide each term in $3 y = 1$ by $3$ .

$\frac{3 y}{3} = \frac{1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{1}{3}$

Divide $y$ by $1$ .

$y = \frac{1}{3}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{3})$

List the intersections.

x-intercept(s): $(\frac{1}{10}, 0)$

y-intercept(s): $(0, \frac{1}{3})$