Find the x and y Intercepts 5x+4y=-6

$5 x + 4 y = - 6$

Step 1

Find the x-intercepts.

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

$5 x + 4 (0) = - 6$

Solve the equation.

Simplify $5 x + 4 (0)$ .

Multiply $4$ by $0$ .

$5 x + 0 = - 6$

Add $5 x$ and $0$ .

$5 x = - 6$

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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 $y$ .

$5 (0) + 4 y = - 6$

Solve the equation.

Simplify $5 (0) + 4 y$ .

Multiply $5$ by $0$ .

$0 + 4 y = - 6$

Add $0$ and $4 y$ .

$4 y = - 6$

Divide each term in $4 y = - 6$ by $4$ and simplify.

Divide each term in $4 y = - 6$ by $4$ .

$\frac{4 y}{4} = \frac{- 6}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 6}{4}$

Divide $y$ by $1$ .

$y = \frac{- 6}{4}$

Simplify the right side.

Cancel the common factor of $- 6$ and $4$ .

Factor $2$ out of $- 6$ .

$y = \frac{2 (- 3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = \frac{2 \cdot - 3}{2 \cdot 2}$

Cancel the common factor.

$y = \frac{2 \cdot - 3}{2 \cdot 2}$

Rewrite the expression.

$y = \frac{- 3}{2}$

Move the negative in front of the fraction.

$y = - \frac{3}{2}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{3}{2})$

Step 3

List the intersections.

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

y-intercept(s): $(0, - \frac{3}{2})$

Step 4

Find the x and y Intercepts 5x+4y=-6

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