Graph y+3=-2/3(x-4)

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

Step 1

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

Subtract $3$ from both sides of the equation.

$y = - \frac{2 x}{3} + \frac{8}{3} - 3$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{2 x}{3} + \frac{8}{3} - 3 \cdot \frac{3}{3}$

Combine $- 3$ and $\frac{3}{3}$ .

$y = - \frac{2 x}{3} + \frac{8}{3} + \frac{- 3 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = - \frac{2 x}{3} + \frac{8 - 3 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 3$ by $3$ .

$y = - \frac{2 x}{3} + \frac{8 - 9}{3}$

Subtract $9$ from $8$ .

$y = - \frac{2 x}{3} + \frac{- 1}{3}$

Move the negative in front of the fraction.

$y = - \frac{2 x}{3} - \frac{1}{3}$

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.

$y = m x + b$

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

Reorder terms.

$y = - (\frac{2}{3} x) - \frac{1}{3}$

Remove parentheses.

$y = - \frac{2}{3} x - \frac{1}{3}$

Step 3

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

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

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

$b = - \frac{1}{3}$

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

Slope: $- \frac{2}{3}$

y-intercept: $(0, - \frac{1}{3})$

Slope: $- \frac{2}{3}$

y-intercept: $(0, - \frac{1}{3})$

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 terms.

$y = - (\frac{2}{3} x) - \frac{1}{3}$

Remove parentheses.

$y = - \frac{2}{3} x - \frac{1}{3}$

Find the x-intercept.

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

$0 = - \frac{2}{3} x - \frac{1}{3}$

Solve the equation.

Rewrite the equation as $- \frac{2}{3} x - \frac{1}{3} = 0$ .

$- \frac{2}{3} x - \frac{1}{3} = 0$

Simplify each term.

Combine $x$ and $\frac{2}{3}$ .

$- \frac{x \cdot 2}{3} - \frac{1}{3} = 0$

Move $2$ to the left of $x$ .

$- \frac{2 x}{3} - \frac{1}{3} = 0$

Add $\frac{1}{3}$ to both sides of the equation.

$- \frac{2 x}{3} = \frac{1}{3}$

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

$- 2 x = 1$

Divide each term in $- 2 x = 1$ by $- 2$ and simplify.

Divide each term in $- 2 x = 1$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{1}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{1}{- 2}$

Divide $x$ by $1$ .

$x = \frac{1}{- 2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{1}{2}, 0)$

Find the y-intercept.

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

$y = - \frac{2}{3} \cdot 0 - \frac{1}{3}$

Solve the equation.

Remove parentheses.

$y = - \frac{2}{3} \cdot 0 - \frac{1}{3}$

Simplify $- \frac{2}{3} \cdot 0 - \frac{1}{3}$ .

Multiply $- \frac{2}{3} \cdot 0$ .

Multiply $0$ by $- 1$ .

$y = 0 (\frac{2}{3}) - \frac{1}{3}$

Multiply $0$ by $\frac{2}{3}$ .

$y = 0 - \frac{1}{3}$

Subtract $\frac{1}{3}$ from $0$ .

$y = - \frac{1}{3}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{3})$

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

$\begin{array}{c} x & y \\ - \frac{1}{2} & 0 \\ 0 & - \frac{1}{3} \end{array}$

Step 5

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

Slope: $- \frac{2}{3}$

y-intercept: $(0, - \frac{1}{3})$

$\begin{array}{c} x & y \\ - \frac{1}{2} & 0 \\ 0 & - \frac{1}{3} \end{array}$

Step 6

Graph y+3=-2/3(x-4)

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