Pre-Algebra Examples

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

Step 1

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

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Step 1.1

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 1.2

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

$m = 2$

$b = \frac{3}{4}$

Step 1.3

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

Slope: $2$

y-intercept: $(0, \frac{3}{4})$

Slope: $2$

y-intercept: $(0, \frac{3}{4})$

Step 2

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 2.1

Find the x-intercept.

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Step 2.1.1

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

$0 = 2 x + \frac{3}{4}$

Step 2.1.2

Solve the equation.

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Step 2.1.2.1

Rewrite the equation as $2 x + \frac{3}{4} = 0$ .

$2 x + \frac{3}{4} = 0$

Step 2.1.2.2

Subtract $\frac{3}{4}$ from both sides of the equation.

$2 x = - \frac{3}{4}$

Step 2.1.2.3

Divide each term in $2 x = - \frac{3}{4}$ by $2$ and simplify.

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Step 2.1.2.3.1

Divide each term in $2 x = - \frac{3}{4}$ by $2$ .

$\frac{2 x}{2} = \frac{- \frac{3}{4}}{2}$

Step 2.1.2.3.2

Simplify the left side.

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Step 2.1.2.3.2.1

Cancel the common factor of $2$ .

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Step 2.1.2.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- \frac{3}{4}}{2}$

Step 2.1.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{3}{4}}{2}$

Step 2.1.2.3.3

Simplify the right side.

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Step 2.1.2.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{3}{4} \cdot \frac{1}{2}$

Step 2.1.2.3.3.2

Multiply $- \frac{3}{4} \cdot \frac{1}{2}$ .

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Step 2.1.2.3.3.2.1

Multiply $\frac{1}{2}$ by $\frac{3}{4}$ .

$x = - \frac{3}{2 \cdot 4}$

Step 2.1.2.3.3.2.2

Multiply $2$ by $4$ .

$x = - \frac{3}{8}$

Step 2.1.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{3}{8}, 0)$

Step 2.2

Find the y-intercept.

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Step 2.2.1

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

$y = 2 (0) + \frac{3}{4}$

Step 2.2.2

Solve the equation.

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Step 2.2.2.1

Remove parentheses.

$y = 2 (0) + \frac{3}{4}$

Step 2.2.2.2

Simplify $2 (0) + \frac{3}{4}$ .

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Step 2.2.2.2.1

Multiply $2$ by $0$ .

$y = 0 + \frac{3}{4}$

Step 2.2.2.2.2

Add $0$ and $\frac{3}{4}$ .

$y = \frac{3}{4}$

Step 2.2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{3}{4})$

Step 2.3

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

$\begin{array}{c} x & y \\ - \frac{3}{8} & 0 \\ 0 & \frac{3}{4} \end{array}$

Step 3

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

Slope: $2$

y-intercept: $(0, \frac{3}{4})$

$\begin{array}{c} x & y \\ - \frac{3}{8} & 0 \\ 0 & \frac{3}{4} \end{array}$

Step 4