Precalculus Examples

$y = x - 2$

Choose a point that the parallel 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 $1$ .

$m = 1$

To find an equation that is parallel to $y = x - 2$ , the slopes must be equal. Using the slope of the equation, find the parallel line using the point-slope formula.

$(0, 0)$

$m = 1$

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.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$(0) = (1) \cdot (0) + b$

Find the value of $b$ .

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Rewrite the equation as $(1) \cdot (0) + b = 0$ .

$(1) \cdot (0) + b = 0$

Simplify the left side.

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Multiply $0$ by $1$ 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.

$y = x$

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Precalculus Examples

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