Algebra Examples

$x + y = 8$

Step 1

Choose a point that the perpendicular line will pass through.

$(0, 0)$

Step 2

Subtract $x$ from both sides of the equation.

$y = 8 - x$

Step 3

Find the slope when $y = 8 - x$ .

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Step 3.1

Rewrite in slope-intercept form.

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Step 3.1.1

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 3.1.2

Reorder $8$ and $- x$ .

$y = - x + 8$

Step 3.2

Using the slope-intercept form, the slope is $- 1$ .

$m = - 1$

Step 4

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- 1}$

Step 5

Simplify $- \frac{1}{- 1}$ to find the slope of the perpendicular line.

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Step 5.1

Divide $1$ by $- 1$ .

$m_{perpendicular} = 1$

Step 5.2

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1$

Step 6

Find the equation of the perpendicular line using the point-slope formula.

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Step 6.1

Use the slope $1$ and a given point $(0, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

Step 6.2

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

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

Step 7

Solve for $y$ .

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Step 7.1

Add $y$ and $0$ .

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

Step 7.2

Simplify $1 \cdot (x + 0)$ .

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Step 7.2.1

Multiply $x + 0$ by $1$ .

$y = x + 0$

Step 7.2.2

Add $x$ and $0$ .

$y = x$

Step 8