Algebra Examples

$(1, - 7)$ , $m = 12$

Step 1

Use the slope $12$ and a given point $(1, - 7)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 7) = 12 \cdot (x - (1))$

Step 2

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

$y + 7 = 12 \cdot (x - 1)$

Step 3

Solve for $y$ .

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Step 3.1

Simplify $12 \cdot (x - 1)$ .

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Step 3.1.1

Rewrite.

$y + 7 = 0 + 0 + 12 \cdot (x - 1)$

Step 3.1.2

Simplify by adding zeros.

$y + 7 = 12 \cdot (x - 1)$

Step 3.1.3

Apply the distributive property.

$y + 7 = 12 x + 12 \cdot - 1$

Step 3.1.4

Multiply $12$ by $- 1$ .

$y + 7 = 12 x - 12$

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.

$y = 12 x - 12 - 7$

Step 3.2.2

Subtract $7$ from $- 12$ .

$y = 12 x - 19$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = 12 x - 19$

Point-slope form:

$y + 7 = 12 \cdot (x - 1)$

Step 5

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