Find the x and y Intercepts 5x-9=-8y-3

$5 x - 9 = - 8 y - 3$

Step 1

Find the x-intercepts.

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

$5 x - 9 = - 8 \cdot 0 - 3$

Solve the equation.

Simplify $- 8 \cdot 0 - 3$ .

Multiply $- 8$ by $0$ .

$5 x - 9 = 0 - 3$

Subtract $3$ from $0$ .

$5 x - 9 = - 3$

Move all terms not containing $x$ to the right side of the equation.

Add $9$ to both sides of the equation.

$5 x = - 3 + 9$

Add $- 3$ and $9$ .

$5 x = 6$

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 $1$ .

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

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 $y$ .

$5 (0) - 9 = - 8 y - 3$

Solve the equation.

Rewrite the equation as $- 8 y - 3 = 5 (0) - 9$ .

$- 8 y - 3 = 5 (0) - 9$

Simplify $5 (0) - 9$ .

Multiply $5$ by $0$ .

$- 8 y - 3 = 0 - 9$

Subtract $9$ from $0$ .

$- 8 y - 3 = - 9$

Move all terms not containing $y$ to the right side of the equation.

Add $3$ to both sides of the equation.

$- 8 y = - 9 + 3$

Add $- 9$ and $3$ .

$- 8 y = - 6$

Divide each term in $- 8 y = - 6$ by $- 8$ and simplify.

Divide each term in $- 8 y = - 6$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 6}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 6}{- 8}$

Divide $y$ by $1$ .

$y = \frac{- 6}{- 8}$

Simplify the right side.

Cancel the common factor of $- 6$ and $- 8$ .

Factor $- 2$ out of $- 6$ .

$y = \frac{- 2 (3)}{- 8}$

Cancel the common factors.

Factor $- 2$ out of $- 8$ .

$y = \frac{- 2 \cdot 3}{- 2 \cdot 4}$

Cancel the common factor.

$y = \frac{- 2 \cdot 3}{- 2 \cdot 4}$

Rewrite the expression.

$y = \frac{3}{4}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{3}{4})$

Step 3

List the intersections.

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

y-intercept(s): $(0, \frac{3}{4})$

Step 4

Find the x and y Intercepts 5x-9=-8y-3

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