Find the x and y Intercepts 5x-6y=30

$5 x - 6 y = 30$

Step 1

Find the x-intercepts.

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

$5 x - 6 \cdot 0 = 30$

Solve the equation.

Simplify $5 x - 6 \cdot 0$ .

Multiply $- 6$ by $0$ .

$5 x + 0 = 30$

Add $5 x$ and $0$ .

$5 x = 30$

Divide each term in $5 x = 30$ by $5$ and simplify.

Divide each term in $5 x = 30$ by $5$ .

$\frac{5 x}{5} = \frac{30}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{30}{5}$

Divide $x$ by $1$ .

$x = \frac{30}{5}$

Simplify the right side.

Divide $30$ by $5$ .

$x = 6$

x-intercept(s) in point form.

x-intercept(s): $(6, 0)$

Step 2

Find the y-intercepts.

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

$5 (0) - 6 y = 30$

Solve the equation.

Simplify $5 (0) - 6 y$ .

Multiply $5$ by $0$ .

$0 - 6 y = 30$

Subtract $6 y$ from $0$ .

$- 6 y = 30$

Divide each term in $- 6 y = 30$ by $- 6$ and simplify.

Divide each term in $- 6 y = 30$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{30}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{30}{- 6}$

Divide $y$ by $1$ .

$y = \frac{30}{- 6}$

Simplify the right side.

Divide $30$ by $- 6$ .

$y = - 5$

y-intercept(s) in point form.

y-intercept(s): $(0, - 5)$

Step 3

List the intersections.

x-intercept(s): $(6, 0)$

y-intercept(s): $(0, - 5)$

Step 4

Find the x and y Intercepts 5x-6y=30

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