Finite Math Examples

$(1, - 1)$ , $m = - \frac{5}{3}$

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.

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

Step 1.3

Substitute the value of $x$ into the equation.

$y = (- \frac{5}{3}) \cdot (1) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$- 1 = (- \frac{5}{3}) \cdot (1) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $- \frac{5}{3} \cdot 1 + b = - 1$ .

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

Step 1.5.2

Multiply $- 1$ by $1$ .

$- \frac{5}{3} + b = - 1$

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

$b = - 1 + \frac{5}{3}$

Step 1.5.3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.5.3.3

Combine $- 1$ and $\frac{3}{3}$ .

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

Step 1.5.3.4

Combine the numerators over the common denominator.

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

Step 1.5.3.5

Simplify the numerator.

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Step 1.5.3.5.1

Multiply $- 1$ by $3$ .

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

Step 1.5.3.5.2

Add $- 3$ and $5$ .

$b = \frac{2}{3}$

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.

$y = - \frac{5}{3} x + \frac{2}{3}$

Step 3