Graph 4x+5y=-9

$4 x + 5 y = - 9$

Step 1

Solve for $y$ .

Subtract $4 x$ from both sides of the equation.

$5 y = - 9 - 4 x$

Divide each term in $5 y = - 9 - 4 x$ by $5$ and simplify.

Divide each term in $5 y = - 9 - 4 x$ by $5$ .

$\frac{5 y}{5} = \frac{- 9}{5} + \frac{- 4 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 9}{5} + \frac{- 4 x}{5}$

Divide $y$ by $1$ .

$y = \frac{- 9}{5} + \frac{- 4 x}{5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{9}{5} + \frac{- 4 x}{5}$

Move the negative in front of the fraction.

$y = - \frac{9}{5} - \frac{4 x}{5}$

Step 2

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Reorder $- \frac{9}{5}$ and $- \frac{4 x}{5}$ .

$y = - \frac{4 x}{5} - \frac{9}{5}$

Write in $y = m x + b$ form.

Reorder terms.

$y = - (\frac{4}{5} x) - \frac{9}{5}$

Remove parentheses.

$y = - \frac{4}{5} x - \frac{9}{5}$

Step 3

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - \frac{4}{5}$

$b = - \frac{9}{5}$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- \frac{4}{5}$

y-intercept: $(0, - \frac{9}{5})$

Slope: $- \frac{4}{5}$

y-intercept: $(0, - \frac{9}{5})$

Step 4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Write in $y = m x + b$ form.

Reorder $- \frac{9}{5}$ and $- \frac{4 x}{5}$ .

$y = - \frac{4 x}{5} - \frac{9}{5}$

Reorder terms.

$y = - (\frac{4}{5} x) - \frac{9}{5}$

Remove parentheses.

$y = - \frac{4}{5} x - \frac{9}{5}$

Find the x-intercept.

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

$0 = - \frac{4}{5} x - \frac{9}{5}$

Solve the equation.

Rewrite the equation as $- \frac{4}{5} x - \frac{9}{5} = 0$ .

$- \frac{4}{5} x - \frac{9}{5} = 0$

Simplify each term.

Combine $x$ and $\frac{4}{5}$ .

$- \frac{x \cdot 4}{5} - \frac{9}{5} = 0$

Move $4$ to the left of $x$ .

$- \frac{4 x}{5} - \frac{9}{5} = 0$

Add $\frac{9}{5}$ to both sides of the equation.

$- \frac{4 x}{5} = \frac{9}{5}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 4 x = 9$

Divide each term in $- 4 x = 9$ by $- 4$ and simplify.

Divide each term in $- 4 x = 9$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{9}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{9}{- 4}$

Divide $x$ by $1$ .

$x = \frac{9}{- 4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{9}{4}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{9}{4}, 0)$

Find the y-intercept.

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

$y = - \frac{4}{5} \cdot 0 - \frac{9}{5}$

Solve the equation.

Remove parentheses.

$y = - \frac{4}{5} \cdot 0 - \frac{9}{5}$

Simplify $- \frac{4}{5} \cdot 0 - \frac{9}{5}$ .

Multiply $- \frac{4}{5} \cdot 0$ .

Multiply $0$ by $- 1$ .

$y = 0 (\frac{4}{5}) - \frac{9}{5}$

Multiply $0$ by $\frac{4}{5}$ .

$y = 0 - \frac{9}{5}$

Subtract $\frac{9}{5}$ from $0$ .

$y = - \frac{9}{5}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{9}{5})$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ - \frac{9}{4} & 0 \\ 0 & - \frac{9}{5} \end{array}$

Step 5

Graph the line using the slope and the y-intercept, or the points.

Slope: $- \frac{4}{5}$

y-intercept: $(0, - \frac{9}{5})$

$\begin{array}{c} x & y \\ - \frac{9}{4} & 0 \\ 0 & - \frac{9}{5} \end{array}$

Step 6

Graph 4x+5y=-9

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