Precalculus Examples

$y = 4 x + 4$ , $y = - x$

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 $4$ .

$m_{1} = 4$

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 $- 1$ .

$m_{2} = - 1$

Set up the system of equations to find any points of intersection.

$y = 4 x + 4$

$y = - x$

Solve the system of equations to find the point of intersection.

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Eliminate the equal sides of each equation and combine.

$4 x + 4 = - x$

Move all terms containing $x$ to the left side of the equation.

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Add $x$ to both sides of the equation.

$4 x + 4 + x = 0$

$y = - x$

Add $4 x$ and $x$ .

$5 x + 4 = 0$

$y = - x$

$5 x + 4 = 0$

$y = - x$

Subtract $4$ from both sides of the equation.

$5 x = - 4$

$y = - x$

Divide each term by $5$ and simplify.

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Divide each term in $5 x = - 4$ by $5$ .

$\frac{5 x}{5} = \frac{- 4}{5}$

$y = - x$

Cancel the common factor of $5$ .

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Cancel the common factor.

$\frac{5 x}{5} = \frac{- 4}{5}$

$y = - x$

Divide $x$ by $1$ .

$x = \frac{- 4}{5}$

$y = - x$

$x = \frac{- 4}{5}$

$y = - x$

Move the negative in front of the fraction.

$x = - \frac{4}{5}$

$y = - x$

$x = - \frac{4}{5}$

$y = - x$

Replace all occurrences of $x$ in $y = - x$ with $- \frac{4}{5}$ .

$x = - \frac{4}{5}$

$y = - (- \frac{4}{5})$

Multiply $- (- \frac{4}{5})$ .

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Multiply $- 1$ by $- 1$ .

$x = - \frac{4}{5}$

$y = 1 (\frac{4}{5})$

Multiply $\frac{4}{5}$ by $1$ .

$x = - \frac{4}{5}$

$y = \frac{4}{5}$

$x = - \frac{4}{5}$

$y = \frac{4}{5}$

The solution to the system of equations can be represented as a point.

$(- \frac{4}{5}, \frac{4}{5})$

Since the slopes are different, the lines will have exactly one intersection point.

$m_{1} = 4$

$m_{2} = - 1$

$(- \frac{4}{5}, \frac{4}{5})$

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