Examples

$(2, 3)$ , $b = 6$

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.

$y = m x + 6$

Step 3

Substitute the value of $x$ into the equation.

$y = m (2) + 6$

Step 4

Substitute the value of $y$ into the equation.

$3 = m (2) + 6$

Step 5

Find the value of $m$ .

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Step 5.1

Rewrite the equation as $m (2) + 6 = 3$ .

$m (2) + 6 = 3$

Step 5.2

Move $2$ to the left of $m$ .

$2 m + 6 = 3$

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 $6$ from both sides of the equation.

$2 m = 3 - 6$

Step 5.3.2

Subtract $6$ from $3$ .

$2 m = - 3$

Step 5.4

Divide each term in $2 m = - 3$ by $2$ and simplify.

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Step 5.4.1

Divide each term in $2 m = - 3$ by $2$ .

$\frac{2 m}{2} = \frac{- 3}{2}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of $2$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{2 m}{2} = \frac{- 3}{2}$

Step 5.4.2.1.2

Divide $m$ by $1$ .

$m = \frac{- 3}{2}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Move the negative in front of the fraction.

$m = - \frac{3}{2}$

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.

$y = - \frac{3}{2} x + 6$

Step 7

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