Algebra Examples

What is an equation of the line that passes through the point

(1, 3)

$(1, 3)$ and is parallel to the line

3 x + y = 9

$3 x + y = 9$ ?

Step 1

Write the problem as a mathematical expression.

(1, 3)

$(1, 3)$ ,

3 x + y = 9

$3 x + y = 9$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 2.2

Subtract

3 x

$3 x$ from both sides of the equation.

y = 9 - 3 x

$y = 9 - 3 x$

Step 2.3

Reorder

9

$9$ and

- 3 x

$- 3 x$ .

y = - 3 x + 9

$y = - 3 x + 9$

y = - 3 x + 9

$y = - 3 x + 9$

Step 3

Using the slope-intercept form, the slope is

- 3

$- 3$ .

m = - 3

$m = - 3$

Step 4

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

Step 5

Use the slope

- 3

$- 3$ and a given point

(1, 3)

$(1, 3)$ to substitute for

x_{1}

$x_{1}$ and

y_{1}

$y_{1}$ in the point-slope form

y - y_{1} = m (x - x_{1})

$y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

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

Step 6

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

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

Step 7

Solve for

$y$ .

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Step 7.1

Simplify

$- 3 \cdot (x - 1)$ .

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Step 7.1.1

Rewrite.

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

Step 7.1.2

Simplify by adding zeros.

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

Step 7.1.3

Apply the distributive property.

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

Step 7.1.4

Multiply

$- 3$ by

$- 1$ .

$y - 3 = - 3 x + 3$

Step 7.2

Move all terms not containing

$y$ to the right side of the equation.

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Step 7.2.1

Add

$3$ to both sides of the equation.

$y = - 3 x + 3 + 3$

Step 7.2.2

Add

$3$ and

$3$ .

$y = - 3 x + 6$

Step 8