Algebra Examples

$(5, - 1)$ , $m = \frac{1}{5}$

Step 1

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

$y - (- 1) = \frac{1}{5} \cdot (x - (5))$

Step 2

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

$y + 1 = \frac{1}{5} \cdot (x - 5)$

Step 3

Solve for $y$ .

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Step 3.1

Simplify $\frac{1}{5} \cdot (x - 5)$ .

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Step 3.1.1

Rewrite.

$y + 1 = 0 + 0 + \frac{1}{5} \cdot (x - 5)$

Step 3.1.2

Simplify by adding zeros.

$y + 1 = \frac{1}{5} \cdot (x - 5)$

Step 3.1.3

Apply the distributive property.

$y + 1 = \frac{1}{5} x + \frac{1}{5} \cdot - 5$

Step 3.1.4

Combine $\frac{1}{5}$ and $x$ .

$y + 1 = \frac{x}{5} + \frac{1}{5} \cdot - 5$

Step 3.1.5

Cancel the common factor of $5$ .

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Step 3.1.5.1

Factor $5$ out of $- 5$ .

$y + 1 = \frac{x}{5} + \frac{1}{5} \cdot (5 (- 1))$

Step 3.1.5.2

Cancel the common factor.

$y + 1 = \frac{x}{5} + \frac{1}{5} \cdot (5 \cdot - 1)$

Step 3.1.5.3

Rewrite the expression.

$y + 1 = \frac{x}{5} - 1$

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 $1$ from both sides of the equation.

$y = \frac{x}{5} - 1 - 1$

Step 3.2.2

Subtract $1$ from $- 1$ .

$y = \frac{x}{5} - 2$

Step 3.3

Reorder terms.

$y = \frac{1}{5} x - 2$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = \frac{1}{5} x - 2$

Point-slope form:

$y + 1 = \frac{1}{5} \cdot (x - 5)$

Step 5