Algebra Examples

$(- 6, 6)$ , $m = \frac{12}{5}$

Step 1

Find the value of $b$ using the formula for the equation of a line.

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Step 1.1

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Step 1.2

Substitute the value of $m$ into the equation.

$y = (\frac{12}{5}) x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (\frac{12}{5}) \cdot (- 6) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$6 = (\frac{12}{5}) \cdot (- 6) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $\frac{12}{5} \cdot - 6 + b = 6$ .

$\frac{12}{5} \cdot - 6 + b = 6$

Step 1.5.2

Simplify each term.

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Step 1.5.2.1

Multiply $\frac{12}{5} \cdot - 6$ .

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Step 1.5.2.1.1

Combine $\frac{12}{5}$ and $- 6$ .

$\frac{12 \cdot - 6}{5} + b = 6$

Step 1.5.2.1.2

Multiply $12$ by $- 6$ .

$\frac{- 72}{5} + b = 6$

Step 1.5.2.2

Move the negative in front of the fraction.

$- \frac{72}{5} + b = 6$

Step 1.5.3

Move all terms not containing $b$ to the right side of the equation.

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Step 1.5.3.1

Add $\frac{72}{5}$ to both sides of the equation.

$b = 6 + \frac{72}{5}$

Step 1.5.3.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = 6 \cdot \frac{5}{5} + \frac{72}{5}$

Step 1.5.3.3

Combine $6$ and $\frac{5}{5}$ .

$b = \frac{6 \cdot 5}{5} + \frac{72}{5}$

Step 1.5.3.4

Combine the numerators over the common denominator.

$b = \frac{6 \cdot 5 + 72}{5}$

Step 1.5.3.5

Simplify the numerator.

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Step 1.5.3.5.1

Multiply $6$ by $5$ .

$b = \frac{30 + 72}{5}$

Step 1.5.3.5.2

Add $30$ and $72$ .

$b = \frac{102}{5}$

Step 2

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = \frac{12}{5} x + \frac{102}{5}$

Step 3

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