Precalculus Examples

$y = 1$ , $y = x + 3$

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 $0$ .

$m_{1} = 0$

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 $1$ .

$m_{2} = 1$

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

$y = 1$

$y = x + 3$

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

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Eliminate the equal sides of each equation and combine.

$1 = x + 3$

Rewrite the equation as $x + 3 = 1$ .

$x + 3 = 1$

$y = x + 3$

Move all terms not containing $x$ to the right side of the equation.

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Subtract $3$ from both sides of the equation.

$x = - 3 + 1$

$y = x + 3$

Add $- 3$ and $1$ .

$x = - 2$

$y = x + 3$

$x = - 2$

$y = x + 3$

Solve for $x$ in the first equation.

$x = - 2 y = x + 3$

Replace all occurrences of $x$ with the solution found by solving the last equation for $x$ . In this case, the value substituted is $- 2$ .

$x = - 2$

$y = (- 2) + 3$

Add $- 2$ and $3$ .

$x = - 2$

$y = 1$

Solve for $y$ in the second equation.

$x = - 2 y = 1$

List the solutions to the system of equations.

$x = - 2$

$y = 1$

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

$(- 2, 1)$

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

$m_{1} = 0$

$m_{2} = 1$

$(- 2, 1)$

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