Algebra Examples

$(9, - 1)$ $m = \frac{4}{3}$

Step 1

Use the slope $\frac{4}{3}$ and a given point $(9, - 1)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 1) = \frac{4}{3} \cdot (x - (9))$

Step 2

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

$y + 1 = \frac{4}{3} \cdot (x - 9)$

Step 3

Solve for $y$ .

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Step 3.1

Simplify $\frac{4}{3} \cdot (x - 9)$ .

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Step 3.1.1

Rewrite.

$y + 1 = 0 + 0 + \frac{4}{3} \cdot (x - 9)$

Step 3.1.2

Simplify by adding zeros.

$y + 1 = \frac{4}{3} \cdot (x - 9)$

Step 3.1.3

Apply the distributive property.

$y + 1 = \frac{4}{3} x + \frac{4}{3} \cdot - 9$

Step 3.1.4

Combine $\frac{4}{3}$ and $x$ .

$y + 1 = \frac{4 x}{3} + \frac{4}{3} \cdot - 9$

Step 3.1.5

Cancel the common factor of $3$ .

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Step 3.1.5.1

Factor $3$ out of $- 9$ .

$y + 1 = \frac{4 x}{3} + \frac{4}{3} \cdot (3 (- 3))$

Step 3.1.5.2

Cancel the common factor.

$y + 1 = \frac{4 x}{3} + \frac{4}{3} \cdot (3 \cdot - 3)$

Step 3.1.5.3

Rewrite the expression.

$y + 1 = \frac{4 x}{3} + 4 \cdot - 3$

Step 3.1.6

Multiply $4$ by $- 3$ .

$y + 1 = \frac{4 x}{3} - 12$

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 $1$ from both sides of the equation.

$y = \frac{4 x}{3} - 12 - 1$

Step 3.2.2

Subtract $1$ from $- 12$ .

$y = \frac{4 x}{3} - 13$

Step 3.3

Reorder terms.

$y = \frac{4}{3} x - 13$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = \frac{4}{3} x - 13$

Point-slope form:

$y + 1 = \frac{4}{3} \cdot (x - 9)$

Step 5