Graph Graph 9x+15y=45

Graph $9 x + 15 y = 45$

Step 1

Solve for $y$ .

Subtract $9 x$ from both sides of the equation.

$15 y = 45 - 9 x$

Divide each term in $15 y = 45 - 9 x$ by $15$ and simplify.

Divide each term in $15 y = 45 - 9 x$ by $15$ .

$\frac{15 y}{15} = \frac{45}{15} + \frac{- 9 x}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 y}{15} = \frac{45}{15} + \frac{- 9 x}{15}$

Divide $y$ by $1$ .

$y = \frac{45}{15} + \frac{- 9 x}{15}$

Simplify the right side.

Simplify each term.

Divide $45$ by $15$ .

$y = 3 + \frac{- 9 x}{15}$

Cancel the common factor of $- 9$ and $15$ .

Factor $3$ out of $- 9 x$ .

$y = 3 + \frac{3 (- 3 x)}{15}$

Cancel the common factors.

Factor $3$ out of $15$ .

$y = 3 + \frac{3 (- 3 x)}{3 (5)}$

Cancel the common factor.

$y = 3 + \frac{3 (- 3 x)}{3 \cdot 5}$

Rewrite the expression.

$y = 3 + \frac{- 3 x}{5}$

Move the negative in front of the fraction.

$y = 3 - \frac{3 x}{5}$

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 $3$ and $- \frac{3 x}{5}$ .

$y = - \frac{3 x}{5} + 3$

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

Reorder terms.

$y = - (\frac{3}{5} x) + 3$

Remove parentheses.

$y = - \frac{3}{5} x + 3$

Step 3

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

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

$m = - \frac{3}{5}$

$b = 3$

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

Slope: $- \frac{3}{5}$

y-intercept: $(0, 3)$

Slope: $- \frac{3}{5}$

y-intercept: $(0, 3)$

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 $3$ and $- \frac{3 x}{5}$ .

$y = - \frac{3 x}{5} + 3$

Reorder terms.

$y = - (\frac{3}{5} x) + 3$

Remove parentheses.

$y = - \frac{3}{5} x + 3$

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

$\begin{array}{c} x & y \\ 0 & 3 \\ 5 & 0 \end{array}$

Step 5

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

Slope: $- \frac{3}{5}$

y-intercept: $(0, 3)$

$\begin{array}{c} x & y \\ 0 & 3 \\ 5 & 0 \end{array}$

Step 6

Graph Graph 9x+15y=45

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