Finite Math Examples

$m = \frac{9}{10}$ , $(7, 6)$

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.

$y = (\frac{9}{10}) x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (\frac{9}{10}) \cdot (7) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$6 = (\frac{9}{10}) \cdot (7) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $\frac{9}{10} \cdot 7 + b = 6$ .

$\frac{9}{10} \cdot 7 + b = 6$

Step 1.5.2

Multiply $\frac{9}{10} \cdot 7$ .

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Step 1.5.2.1

Combine $\frac{9}{10}$ and $7$ .

$\frac{9 \cdot 7}{10} + b = 6$

Step 1.5.2.2

Multiply $9$ by $7$ .

$\frac{63}{10} + b = 6$

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

Subtract $\frac{63}{10}$ from both sides of the equation.

$b = 6 - \frac{63}{10}$

Step 1.5.3.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$b = 6 \cdot \frac{10}{10} - \frac{63}{10}$

Step 1.5.3.3

Combine $6$ and $\frac{10}{10}$ .

$b = \frac{6 \cdot 10}{10} - \frac{63}{10}$

Step 1.5.3.4

Combine the numerators over the common denominator.

$b = \frac{6 \cdot 10 - 63}{10}$

Step 1.5.3.5

Simplify the numerator.

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Step 1.5.3.5.1

Multiply $6$ by $10$ .

$b = \frac{60 - 63}{10}$

Step 1.5.3.5.2

Subtract $63$ from $60$ .

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

Step 1.5.3.6

Move the negative in front of the fraction.

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

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.

$y = \frac{9}{10} x - \frac{3}{10}$

Step 3