Algebra Examples

$(8, - 1)$ and slope $m = - 3$

Step 1

Use the slope $- 3$ and a given point $(8, - 1)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 1) = - 3 \cdot (x - (8))$

Step 2

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

$y + 1 = - 3 \cdot (x - 8)$

Step 3

Solve for $y$ .

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Step 3.1

Simplify $- 3 \cdot (x - 8)$ .

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Step 3.1.1

Rewrite.

$y + 1 = 0 + 0 - 3 \cdot (x - 8)$

Step 3.1.2

Simplify by adding zeros.

$y + 1 = - 3 \cdot (x - 8)$

Step 3.1.3

Apply the distributive property.

$y + 1 = - 3 x - 3 \cdot - 8$

Step 3.1.4

Multiply $- 3$ by $- 8$ .

$y + 1 = - 3 x + 24$

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.

$y = - 3 x + 24 - 1$

Step 3.2.2

Subtract $1$ from $24$ .

$y = - 3 x + 23$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - 3 x + 23$

Point-slope form:

$y + 1 = - 3 \cdot (x - 8)$

Step 5