Find the Equation with a Point and y-Intercept

$(- 5, - 7)$ , $12$

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.

$y = m x + 12$

Step 3

Substitute the value of $x$ into the equation.

$y = m (- 5) + 12$

Step 4

Substitute the value of $y$ into the equation.

$- 7 = m (- 5) + 12$

Step 5

Find the value of $m$ .

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Step 5.1

Rewrite the equation as $m (- 5) + 12 = - 7$ .

$m (- 5) + 12 = - 7$

Step 5.2

Move $- 5$ to the left of $m$ .

$- 5 m + 12 = - 7$

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 $12$ from both sides of the equation.

$- 5 m = - 7 - 12$

Step 5.3.2

Subtract $12$ from $- 7$ .

$- 5 m = - 19$

Step 5.4

Divide each term in $- 5 m = - 19$ by $- 5$ and simplify.

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Step 5.4.1

Divide each term in $- 5 m = - 19$ by $- 5$ .

$\frac{- 5 m}{- 5} = \frac{- 19}{- 5}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of $- 5$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{- 5 m}{- 5} = \frac{- 19}{- 5}$

Step 5.4.2.1.2

Divide $m$ by $1$ .

$m = \frac{- 19}{- 5}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Dividing two negative values results in a positive value.

$m = \frac{19}{5}$

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.

$y = \frac{19}{5} x + 12$

Step 7

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