Algebra Examples

$17 x + 2 y = 0$

Choose a point that the perpendicular line will pass through.

$(0, 0)$

Solve $y = - \frac{17 x}{2}$ .

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Since $17 x$ does not contain the variable to solve for, move it to the right side of the equation by subtracting $17 x$ from both sides.

$2 y = - 17 x$

Divide each term by $2$ and simplify.

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Divide each term in $2 y = - 17 x$ by $2$ .

$\frac{2 y}{2} = - \frac{17 x}{2}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

$\frac{2 y}{2} = - \frac{17 x}{2}$

Divide $y$ by $1$ to get $y$ .

$y = - \frac{17 x}{2}$

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 $- \frac{17}{2}$ .

$m = - \frac{17}{2}$

The equation of a perpendicular line to $y = - \frac{17 x}{2}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- \frac{17}{2}}$

Simplify $- \frac{1}{- \frac{17}{2}}$ to find the slope of the perpendicular line.

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Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (- \frac{2}{17}))$

Multiply $- \frac{2}{17}$ by $1$ to get $- \frac{2}{17}$ .

$m_{perpendicular} = \frac{2}{17}$

Simplify $- - \frac{2}{17}$ .

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Multiply $- 1$ by $- 1$ to get $1$ .

$m_{perpendicular} = 1 (\frac{2}{17})$

Multiply $\frac{2}{17}$ by $1$ to get $\frac{2}{17}$ .

$m_{perpendicular} = \frac{2}{17}$

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.

$y = (\frac{2}{17}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{2}{17}) \cdot (0) + b$

Substitute the value of $y$ into the equation.

$(0) = (\frac{2}{17}) \cdot (0) + b$

Find the value of $b$ .

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Rewrite the equation as $(\frac{2}{17}) \cdot (0) + b = 0$ .

$(\frac{2}{17}) \cdot (0) + b = 0$

Simplify the left side.

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Simplify each term.

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Multiply $\frac{2}{17}$ by $0$ to get $(\frac{2}{17}) (0)$ .

$(\frac{2}{17}) (0) + b = 0$

Multiply $\frac{2}{17}$ by $0$ to get $0$ .

$0 + b = 0$

Add $0$ and $b$ to get $b$ .

$b = 0$

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.

$y = \frac{2}{17} x$

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