Pre-Algebra Examples

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

Step 1

Subtract $\frac{2}{7}$ from both sides of the equation.

$y = 3 x - \frac{2}{7}$

Step 2

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

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Step 2.1

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

$y = m x + b$

Step 2.2

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

$m = 3$

$b = - \frac{2}{7}$

Step 2.3

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

Slope: $3$

y-intercept: $(0, - \frac{2}{7})$

Slope: $3$

y-intercept: $(0, - \frac{2}{7})$

Step 3

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

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Step 3.1

Find the x-intercept.

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Step 3.1.1

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

$0 = 3 x - \frac{2}{7}$

Step 3.1.2

Solve the equation.

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Step 3.1.2.1

Rewrite the equation as $3 x - \frac{2}{7} = 0$ .

$3 x - \frac{2}{7} = 0$

Step 3.1.2.2

Add $\frac{2}{7}$ to both sides of the equation.

$3 x = \frac{2}{7}$

Step 3.1.2.3

Divide each term in $3 x = \frac{2}{7}$ by $3$ and simplify.

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Step 3.1.2.3.1

Divide each term in $3 x = \frac{2}{7}$ by $3$ .

$\frac{3 x}{3} = \frac{\frac{2}{7}}{3}$

Step 3.1.2.3.2

Simplify the left side.

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Step 3.1.2.3.2.1

Cancel the common factor of $3$ .

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Step 3.1.2.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{\frac{2}{7}}{3}$

Step 3.1.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{2}{7}}{3}$

Step 3.1.2.3.3

Simplify the right side.

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Step 3.1.2.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{2}{7} \cdot \frac{1}{3}$

Step 3.1.2.3.3.2

Multiply $\frac{2}{7} \cdot \frac{1}{3}$ .

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Step 3.1.2.3.3.2.1

Multiply $\frac{2}{7}$ by $\frac{1}{3}$ .

$x = \frac{2}{7 \cdot 3}$

Step 3.1.2.3.3.2.2

Multiply $7$ by $3$ .

$x = \frac{2}{21}$

Step 3.1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{2}{21}, 0)$

Step 3.2

Find the y-intercept.

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Step 3.2.1

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

$y = 3 (0) - \frac{2}{7}$

Step 3.2.2

Solve the equation.

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Step 3.2.2.1

Remove parentheses.

$y = 3 (0) - \frac{2}{7}$

Step 3.2.2.2

Simplify $3 (0) - \frac{2}{7}$ .

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Step 3.2.2.2.1

Multiply $3$ by $0$ .

$y = 0 - \frac{2}{7}$

Step 3.2.2.2.2

Subtract $\frac{2}{7}$ from $0$ .

$y = - \frac{2}{7}$

Step 3.2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{2}{7})$

Step 3.3

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

$\begin{array}{c} x & y \\ 0 & - \frac{2}{7} \\ \frac{2}{21} & 0 \end{array}$

Step 4

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

Slope: $3$

y-intercept: $(0, - \frac{2}{7})$

$\begin{array}{c} x & y \\ 0 & - \frac{2}{7} \\ \frac{2}{21} & 0 \end{array}$

Step 5