Algebra Examples

$(- 3, - 7)$ ; $m = - \frac{6}{5}$

Step 1

Use the slope $- \frac{6}{5}$ and a given point $(- 3, - 7)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 7) = - \frac{6}{5} \cdot (x - (- 3))$

Step 2

Simplify the equation and keep it in point-slope form.

$y + 7 = - \frac{6}{5} \cdot (x + 3)$

Step 3

Solve for $y$ .

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Step 3.1

Simplify $- \frac{6}{5} \cdot (x + 3)$ .

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Step 3.1.1

Rewrite.

$y + 7 = 0 + 0 - \frac{6}{5} \cdot (x + 3)$

Step 3.1.2

Simplify by adding zeros.

$y + 7 = - \frac{6}{5} \cdot (x + 3)$

Step 3.1.3

Apply the distributive property.

$y + 7 = - \frac{6}{5} x - \frac{6}{5} \cdot 3$

Step 3.1.4

Combine $x$ and $\frac{6}{5}$ .

$y + 7 = - \frac{x \cdot 6}{5} - \frac{6}{5} \cdot 3$

Step 3.1.5

Multiply $- \frac{6}{5} \cdot 3$ .

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Step 3.1.5.1

Multiply $3$ by $- 1$ .

$y + 7 = - \frac{x \cdot 6}{5} - 3 (\frac{6}{5})$

Step 3.1.5.2

Combine $- 3$ and $\frac{6}{5}$ .

$y + 7 = - \frac{x \cdot 6}{5} + \frac{- 3 \cdot 6}{5}$

Step 3.1.5.3

Multiply $- 3$ by $6$ .

$y + 7 = - \frac{x \cdot 6}{5} + \frac{- 18}{5}$

Step 3.1.6

Simplify each term.

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Step 3.1.6.1

Move $6$ to the left of $x$ .

$y + 7 = - \frac{6 \cdot x}{5} + \frac{- 18}{5}$

Step 3.1.6.2

Move the negative in front of the fraction.

$y + 7 = - \frac{6 x}{5} - \frac{18}{5}$

Step 3.2

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

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Step 3.2.1

Subtract $7$ from both sides of the equation.

$y = - \frac{6 x}{5} - \frac{18}{5} - 7$

Step 3.2.2

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = - \frac{6 x}{5} - \frac{18}{5} - 7 \cdot \frac{5}{5}$

Step 3.2.3

Combine $- 7$ and $\frac{5}{5}$ .

$y = - \frac{6 x}{5} - \frac{18}{5} + \frac{- 7 \cdot 5}{5}$

Step 3.2.4

Combine the numerators over the common denominator.

$y = - \frac{6 x}{5} + \frac{- 18 - 7 \cdot 5}{5}$

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply $- 7$ by $5$ .

$y = - \frac{6 x}{5} + \frac{- 18 - 35}{5}$

Step 3.2.5.2

Subtract $35$ from $- 18$ .

$y = - \frac{6 x}{5} + \frac{- 53}{5}$

Step 3.2.6

Move the negative in front of the fraction.

$y = - \frac{6 x}{5} - \frac{53}{5}$

Step 3.3

Write in $y = m x + b$ form.

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Step 3.3.1

Reorder terms.

$y = - (\frac{6}{5} x) - \frac{53}{5}$

Step 3.3.2

Remove parentheses.

$y = - \frac{6}{5} x - \frac{53}{5}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - \frac{6}{5} x - \frac{53}{5}$

Point-slope form:

$y + 7 = - \frac{6}{5} \cdot (x + 3)$

Step 5