Finite Math Examples

$m = \frac{2}{3}$ , $(5, - 8)$

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.

$y = (\frac{2}{3}) x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (\frac{2}{3}) \cdot (5) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$- 8 = (\frac{2}{3}) \cdot (5) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $\frac{2}{3} \cdot 5 + b = - 8$ .

$\frac{2}{3} \cdot 5 + b = - 8$

Step 1.5.2

Multiply $\frac{2}{3} \cdot 5$ .

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Step 1.5.2.1

Combine $\frac{2}{3}$ and $5$ .

$\frac{2 \cdot 5}{3} + b = - 8$

Step 1.5.2.2

Multiply $2$ by $5$ .

$\frac{10}{3} + b = - 8$

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

Subtract $\frac{10}{3}$ from both sides of the equation.

$b = - 8 - \frac{10}{3}$

Step 1.5.3.2

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = - 8 \cdot \frac{3}{3} - \frac{10}{3}$

Step 1.5.3.3

Combine $- 8$ and $\frac{3}{3}$ .

$b = \frac{- 8 \cdot 3}{3} - \frac{10}{3}$

Step 1.5.3.4

Combine the numerators over the common denominator.

$b = \frac{- 8 \cdot 3 - 10}{3}$

Step 1.5.3.5

Simplify the numerator.

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Step 1.5.3.5.1

Multiply $- 8$ by $3$ .

$b = \frac{- 24 - 10}{3}$

Step 1.5.3.5.2

Subtract $10$ from $- 24$ .

$b = \frac{- 34}{3}$

Step 1.5.3.6

Move the negative in front of the fraction.

$b = - \frac{34}{3}$

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.

$y = \frac{2}{3} x - \frac{34}{3}$

Step 3