Algebra Examples

$(4, - 6)$ ; $m = \frac{3}{5}$

Step 1

Use the slope $\frac{3}{5}$ and a given point $(4, - 6)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 6) = \frac{3}{5} \cdot (x - (4))$

Step 2

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

$y + 6 = \frac{3}{5} \cdot (x - 4)$

Step 3

Solve for $y$ .

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Step 3.1

Simplify $\frac{3}{5} \cdot (x - 4)$ .

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Step 3.1.1

Rewrite.

$y + 6 = 0 + 0 + \frac{3}{5} \cdot (x - 4)$

Step 3.1.2

Simplify by adding zeros.

$y + 6 = \frac{3}{5} \cdot (x - 4)$

Step 3.1.3

Apply the distributive property.

$y + 6 = \frac{3}{5} x + \frac{3}{5} \cdot - 4$

Step 3.1.4

Combine $\frac{3}{5}$ and $x$ .

$y + 6 = \frac{3 x}{5} + \frac{3}{5} \cdot - 4$

Step 3.1.5

Multiply $\frac{3}{5} \cdot - 4$ .

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Step 3.1.5.1

Combine $\frac{3}{5}$ and $- 4$ .

$y + 6 = \frac{3 x}{5} + \frac{3 \cdot - 4}{5}$

Step 3.1.5.2

Multiply $3$ by $- 4$ .

$y + 6 = \frac{3 x}{5} + \frac{- 12}{5}$

Step 3.1.6

Move the negative in front of the fraction.

$y + 6 = \frac{3 x}{5} - \frac{12}{5}$

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 $6$ from both sides of the equation.

$y = \frac{3 x}{5} - \frac{12}{5} - 6$

Step 3.2.2

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = \frac{3 x}{5} - \frac{12}{5} - 6 \cdot \frac{5}{5}$

Step 3.2.3

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

$y = \frac{3 x}{5} - \frac{12}{5} + \frac{- 6 \cdot 5}{5}$

Step 3.2.4

Combine the numerators over the common denominator.

$y = \frac{3 x}{5} + \frac{- 12 - 6 \cdot 5}{5}$

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply $- 6$ by $5$ .

$y = \frac{3 x}{5} + \frac{- 12 - 30}{5}$

Step 3.2.5.2

Subtract $30$ from $- 12$ .

$y = \frac{3 x}{5} + \frac{- 42}{5}$

Step 3.2.6

Move the negative in front of the fraction.

$y = \frac{3 x}{5} - \frac{42}{5}$

Step 3.3

Reorder terms.

$y = \frac{3}{5} x - \frac{42}{5}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = \frac{3}{5} x - \frac{42}{5}$

Point-slope form:

$y + 6 = \frac{3}{5} \cdot (x - 4)$

Step 5