Algebra Examples

$f (x) = \frac{3 x^{2} - 9 x + 6}{5 x - 10}$

Step 1

Rewrite the function as an equation.

$y = \frac{3 (x - 1)}{5}$

Step 2

Rewrite in slope-intercept form.

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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

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

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Step 2.2.1

Apply the distributive property.

$y = \frac{3 x + 3 \cdot - 1}{5}$

Step 2.2.2

Multiply $3$ by $- 1$ .

$y = \frac{3 x - 3}{5}$

Step 2.2.3

Split the fraction $\frac{3 x - 3}{5}$ into two fractions.

$y = \frac{3 x}{5} + \frac{- 3}{5}$

Step 2.2.4

Move the negative in front of the fraction.

$y = \frac{3 x}{5} - \frac{3}{5}$

Step 2.2.5

Reorder terms.

$y = \frac{3}{5} x - \frac{3}{5}$

Step 3

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

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Step 3.1

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

$m = \frac{3}{5}$

$b = - \frac{3}{5}$

Step 3.2

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

Slope: $\frac{3}{5}$

y-intercept: $(0, - \frac{3}{5})$

Slope: $\frac{3}{5}$

y-intercept: $(0, - \frac{3}{5})$

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.

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Step 4.1

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

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Step 4.1.1

Apply the distributive property.

$y = \frac{3 x + 3 \cdot - 1}{5}$

Step 4.1.2

Multiply $3$ by $- 1$ .

$y = \frac{3 x - 3}{5}$

Step 4.1.3

Split the fraction $\frac{3 x - 3}{5}$ into two fractions.

$y = \frac{3 x}{5} + \frac{- 3}{5}$

Step 4.1.4

Move the negative in front of the fraction.

$y = \frac{3 x}{5} - \frac{3}{5}$

Step 4.1.5

Reorder terms.

$y = \frac{3}{5} x - \frac{3}{5}$

Step 4.2

Find the x-intercept.

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Step 4.2.1

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

$0 = \frac{3}{5} x - \frac{3}{5}$

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

Rewrite the equation as $\frac{3}{5} x - \frac{3}{5} = 0$ .

$\frac{3}{5} x - \frac{3}{5} = 0$

Step 4.2.2.2

Combine $\frac{3}{5}$ and $x$ .

$\frac{3 x}{5} - \frac{3}{5} = 0$

Step 4.2.2.3

Add $\frac{3}{5}$ to both sides of the equation.

$\frac{3 x}{5} = \frac{3}{5}$

Step 4.2.2.4

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

$3 x = 3$

Step 4.2.2.5

Divide each term in $3 x = 3$ by $3$ and simplify.

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Step 4.2.2.5.1

Divide each term in $3 x = 3$ by $3$ .

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

Step 4.2.2.5.2

Simplify the left side.

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Step 4.2.2.5.2.1

Cancel the common factor of $3$ .

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Step 4.2.2.5.2.1.1

Cancel the common factor.

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

Step 4.2.2.5.2.1.2

Divide $x$ by $1$ .

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

Step 4.2.2.5.3

Simplify the right side.

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Step 4.2.2.5.3.1

Divide $3$ by $3$ .

$x = 1$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s): $(1, 0)$

Step 4.3

Find the y-intercept.

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Step 4.3.1

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

$y = \frac{3}{5} \cdot (0) - \frac{3}{5}$

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

Multiply $\frac{3}{5}$ by $0$ .

$y = \frac{3}{5} \cdot 0 - \frac{3}{5}$

Step 4.3.2.2

Remove parentheses.

$y = \frac{3}{5} \cdot (0) - \frac{3}{5}$

Step 4.3.2.3

Simplify $\frac{3}{5} \cdot (0) - \frac{3}{5}$ .

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Step 4.3.2.3.1

Multiply $\frac{3}{5}$ by $0$ .

$y = 0 - \frac{3}{5}$

Step 4.3.2.3.2

Subtract $\frac{3}{5}$ from $0$ .

$y = - \frac{3}{5}$

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{3}{5})$

Step 4.4

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

$\begin{array}{c} x & y \\ 0 & - \frac{3}{5} \\ 1 & 0 \end{array}$

Step 5

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

Slope: $\frac{3}{5}$

y-intercept: $(0, - \frac{3}{5})$

$\begin{array}{c} x & y \\ 0 & - \frac{3}{5} \\ 1 & 0 \end{array}$

Step 6