Algebra Examples

through: $(- 3, - 3)$ ; parallel to $y = \frac{7}{3} x + 3$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Simplify the right side.

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Step 1.2.1

Combine $\frac{7}{3}$ and $x$ .

$y = \frac{7 x}{3} + 3$

Step 1.3

Reorder terms.

$y = \frac{7}{3} x + 3$

Step 2

Using the slope-intercept form, the slope is $\frac{7}{3}$ .

$m = \frac{7}{3}$

Step 3

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Step 4

Use the slope $\frac{7}{3}$ and a given point $(- 3, - 3)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 3) = \frac{7}{3} \cdot (x - (- 3))$

Step 5

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

$y + 3 = \frac{7}{3} \cdot (x + 3)$

Step 6

Solve for $y$ .

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Step 6.1

Simplify $\frac{7}{3} \cdot (x + 3)$ .

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Step 6.1.1

Rewrite.

$y + 3 = 0 + 0 + \frac{7}{3} \cdot (x + 3)$

Step 6.1.2

Simplify by adding zeros.

$y + 3 = \frac{7}{3} \cdot (x + 3)$

Step 6.1.3

Apply the distributive property.

$y + 3 = \frac{7}{3} x + \frac{7}{3} \cdot 3$

Step 6.1.4

Combine $\frac{7}{3}$ and $x$ .

$y + 3 = \frac{7 x}{3} + \frac{7}{3} \cdot 3$

Step 6.1.5

Cancel the common factor of $3$ .

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Step 6.1.5.1

Cancel the common factor.

$y + 3 = \frac{7 x}{3} + \frac{7}{3} \cdot 3$

Step 6.1.5.2

Rewrite the expression.

$y + 3 = \frac{7 x}{3} + 7$

Step 6.2

Move all terms not containing $y$ to the right side of the equation.

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Step 6.2.1

Subtract $3$ from both sides of the equation.

$y = \frac{7 x}{3} + 7 - 3$

Step 6.2.2

Subtract $3$ from $7$ .

$y = \frac{7 x}{3} + 4$

Step 6.3

Reorder terms.

$y = \frac{7}{3} x + 4$

Step 7