Find the x and y Intercepts What is the y-intercept of the equation 10x+3y=12 ?

What is the y-intercept of the equation $10 x + 3 y = 12$ ?

Step 1

Find the x-intercepts.

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

$10 x + 3 (0) = 12$

Solve the equation.

Simplify $10 x + 3 (0)$ .

Multiply $3$ by $0$ .

$10 x + 0 = 12$

Add $10 x$ and $0$ .

$10 x = 12$

Divide each term in $10 x = 12$ by $10$ and simplify.

Divide each term in $10 x = 12$ by $10$ .

$\frac{10 x}{10} = \frac{12}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{12}{10}$

Divide $x$ by $1$ .

$x = \frac{12}{10}$

Simplify the right side.

Cancel the common factor of $12$ and $10$ .

Factor $2$ out of $12$ .

$x = \frac{2 (6)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$x = \frac{2 \cdot 6}{2 \cdot 5}$

Cancel the common factor.

$x = \frac{2 \cdot 6}{2 \cdot 5}$

Rewrite the expression.

$x = \frac{6}{5}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{6}{5}, 0)$

Step 2

Find the y-intercepts.

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

$10 (0) + 3 y = 12$

Solve the equation.

Simplify $10 (0) + 3 y$ .

Multiply $10$ by $0$ .

$0 + 3 y = 12$

Add $0$ and $3 y$ .

$3 y = 12$

Divide each term in $3 y = 12$ by $3$ and simplify.

Divide each term in $3 y = 12$ by $3$ .

$\frac{3 y}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{12}{3}$

Divide $y$ by $1$ .

$y = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$y = 4$

y-intercept(s) in point form.

y-intercept(s): $(0, 4)$

Step 3

List the intersections.

x-intercept(s): $(\frac{6}{5}, 0)$

y-intercept(s): $(0, 4)$

Step 4

Find the x and y Intercepts What is the y-intercept of the equation 10x+3y=12 ?

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