Find the x and y Intercepts 2x+5y=-6

$2 x + 5 y = - 6$

Step 1

Find the x-intercepts.

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

$2 x + 5 (0) = - 6$

Solve the equation.

Simplify $2 x + 5 (0)$ .

Multiply $5$ by $0$ .

$2 x + 0 = - 6$

Add $2 x$ and $0$ .

$2 x = - 6$

Divide each term in $2 x = - 6$ by $2$ and simplify.

Divide each term in $2 x = - 6$ by $2$ .

$\frac{2 x}{2} = \frac{- 6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 6}{2}$

Divide $x$ by $1$ .

$x = \frac{- 6}{2}$

Simplify the right side.

Divide $- 6$ by $2$ .

$x = - 3$

x-intercept(s) in point form.

x-intercept(s): $(- 3, 0)$

Step 2

Find the y-intercepts.

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

$2 (0) + 5 y = - 6$

Solve the equation.

Simplify $2 (0) + 5 y$ .

Multiply $2$ by $0$ .

$0 + 5 y = - 6$

Add $0$ and $5 y$ .

$5 y = - 6$

Divide each term in $5 y = - 6$ by $5$ and simplify.

Divide each term in $5 y = - 6$ by $5$ .

$\frac{5 y}{5} = \frac{- 6}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 6}{5}$

Divide $y$ by $1$ .

$y = \frac{- 6}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{6}{5}$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(- 3, 0)$

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

Step 4

Find the x and y Intercepts 2x+5y=-6

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