Pre-Algebra Examples

$\frac{a^{2} - 49}{4 (a - 7)}$

Step 1

Rewrite in slope-intercept form.

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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

Split the fraction $\frac{x + 7}{4}$ into two fractions.

$y = \frac{x}{4} + \frac{7}{4}$

Step 1.3

Reorder terms.

$y = \frac{1}{4} x + \frac{7}{4}$

Step 2

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

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Step 2.1

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

$m = \frac{1}{4}$

$b = \frac{7}{4}$

Step 2.2

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

Slope: $\frac{1}{4}$

y-intercept: $(0, \frac{7}{4})$

Slope: $\frac{1}{4}$

y-intercept: $(0, \frac{7}{4})$

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

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

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Step 3.1.1

Split the fraction $\frac{x + 7}{4}$ into two fractions.

$y = \frac{x}{4} + \frac{7}{4}$

Step 3.1.2

Reorder terms.

$y = \frac{1}{4} x + \frac{7}{4}$

Step 3.2

Find the x-intercept.

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Step 3.2.1

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

$0 = \frac{1}{4} x + \frac{7}{4}$

Step 3.2.2

Solve the equation.

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Step 3.2.2.1

Rewrite the equation as $\frac{1}{4} x + \frac{7}{4} = 0$ .

$\frac{1}{4} x + \frac{7}{4} = 0$

Step 3.2.2.2

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} + \frac{7}{4} = 0$

Step 3.2.2.3

Subtract $\frac{7}{4}$ from both sides of the equation.

$\frac{x}{4} = - \frac{7}{4}$

Step 3.2.2.4

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

$x = - 7$

Step 3.2.3

x-intercept(s) in point form.

x-intercept(s): $(- 7, 0)$

Step 3.3

Find the y-intercept.

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Step 3.3.1

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

$y = \frac{0}{4} + \frac{7}{4}$

Step 3.3.2

Solve the equation.

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Step 3.3.2.1

Remove parentheses.

$y = \frac{0}{4} + \frac{7}{4}$

Step 3.3.2.2

Simplify $\frac{0}{4} + \frac{7}{4}$ .

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Step 3.3.2.2.1

Combine the numerators over the common denominator.

$y = \frac{0 + 7}{4}$

Step 3.3.2.2.2

Add $0$ and $7$ .

$y = \frac{7}{4}$

Step 3.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{7}{4})$

Step 3.4

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

$\begin{array}{c} x & y \\ - 11 & - 1 \\ - 7 & 0 \end{array}$

Step 4

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

Slope: $\frac{1}{4}$

y-intercept: $(0, \frac{7}{4})$

$\begin{array}{c} x & y \\ - 11 & - 1 \\ - 7 & 0 \end{array}$

Step 5