Precalculus Examples

$(- 1, 2)$ , $b = 3$

Step 1

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

$y = m x + b$

Step 2

Substitute the value of $b$ into the equation.

$y = m x + 3$

Step 3

Substitute the value of $x$ into the equation.

$y = m (- 1) + 3$

Step 4

Substitute the value of $y$ into the equation.

$2 = m (- 1) + 3$

Step 5

Find the value of $m$ .

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Step 5.1

Rewrite the equation as $m (- 1) + 3 = 2$ .

$m (- 1) + 3 = 2$

Step 5.2

Simplify each term.

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Step 5.2.1

Move $- 1$ to the left of $m$ .

$- 1 m + 3 = 2$

Step 5.2.2

Rewrite $- 1 m$ as $- m$ .

$- m + 3 = 2$

Step 5.3

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

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Step 5.3.1

Subtract $3$ from both sides of the equation.

$- m = 2 - 3$

Step 5.3.2

Subtract $3$ from $2$ .

$- m = - 1$

Step 5.4

Divide each term in $- m = - 1$ by $- 1$ and simplify.

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Step 5.4.1

Divide each term in $- m = - 1$ by $- 1$ .

$\frac{- m}{- 1} = \frac{- 1}{- 1}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Dividing two negative values results in a positive value.

$\frac{m}{1} = \frac{- 1}{- 1}$

Step 5.4.2.2

Divide $m$ by $1$ .

$m = \frac{- 1}{- 1}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Divide $- 1$ by $- 1$ .

$m = 1$

Step 6

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.

$y = x + 3$

Step 7

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