Graph Graph -14x+21y=84

Graph $- 14 x + 21 y = 84$

Solve for $y$ .

Add $14 x$ to both sides of the equation.

$21 y = 84 + 14 x$

Divide each term in $21 y = 84 + 14 x$ by $21$ and simplify.

Divide each term in $21 y = 84 + 14 x$ by $21$ .

$\frac{21 y}{21} = \frac{84}{21} + \frac{14 x}{21}$

Simplify the left side.

Cancel the common factor of $21$ .

Cancel the common factor.

$\frac{21 y}{21} = \frac{84}{21} + \frac{14 x}{21}$

Divide $y$ by $1$ .

$y = \frac{84}{21} + \frac{14 x}{21}$

Simplify the right side.

Simplify each term.

Divide $84$ by $21$ .

$y = 4 + \frac{14 x}{21}$

Cancel the common factor of $14$ and $21$ .

Factor $7$ out of $14 x$ .

$y = 4 + \frac{7 (2 x)}{21}$

Cancel the common factors.

Factor $7$ out of $21$ .

$y = 4 + \frac{7 (2 x)}{7 (3)}$

Cancel the common factor.

$y = 4 + \frac{7 (2 x)}{7 \cdot 3}$

Rewrite the expression.

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

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 $4$ and $\frac{2 x}{3}$ .

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

Reorder terms.

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

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

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

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

$b = 4$

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: $(0, 4)$

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

y-intercept: $(0, 4)$

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 $4$ and $\frac{2 x}{3}$ .

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

Reorder terms.

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

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

$\begin{array}{c} x & y \\ 0 & 4 \\ 3 & 6 \end{array}$

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

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

y-intercept: $(0, 4)$

$\begin{array}{c} x & y \\ 0 & 4 \\ 3 & 6 \end{array}$

Graph Graph -14x+21y=84

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