Algebra Examples

$y = 5 x + 4$

Choose a point that the perpendicular line will pass through.

$(0, 0)$

Use the slope-intercept form to find the slope.

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

$y = m x + b$

Using the slope-intercept form, the slope is $5$ .

$m = 5$

The equation of a perpendicular line to $y = 5 x + 4$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{5}$

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

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Find the value of $b$ using the formula for the equation of a line.

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Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

$y = (- \frac{1}{5}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{1}{5}) \cdot (0) + b$

Substitute the value of $y$ into the equation.

$(0) = (- \frac{1}{5}) \cdot (0) + b$

Find the value of $b$ .

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Rewrite the equation as $(- \frac{1}{5}) \cdot (0) + b = 0$ .

$(- \frac{1}{5}) \cdot (0) + b = 0$

Simplify the left side.

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Simplify each term.

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Multiply $- \frac{1}{5}$ by $0$ .

$(- \frac{1}{5}) (0) + b = 0$

Simplify $(- \frac{1}{5}) (0)$ .

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Multiply $0$ by $- 1$ .

$0 (\frac{1}{5}) + b = 0$

Multiply $0$ by $\frac{1}{5}$ .

$0 + b = 0$

Add $0$ and $b$ .

$b = 0$

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = - \frac{1}{5} x$

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