Precalculus Examples

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

Step 1

Use the slope-intercept form to find the slope.

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Step 1.1

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

$y = m x + b$

Step 1.2

Using the slope-intercept form, the slope is $0$ .

$m_{1} = 0$

Step 2

Use the slope-intercept form to find the slope.

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Step 2.1

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

$y = m x + b$

Step 2.2

Using the slope-intercept form, the slope is $1$ .

$m_{2} = 1$

Step 3

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

$y = 1, y = x + 3$

Step 4

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

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Step 4.1

Eliminate the equal sides of each equation and combine.

$1 = x + 3$

Step 4.2

Solve $1 = x + 3$ for $x$ .

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Step 4.2.1

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

$x + 3 = 1$

Step 4.2.2

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

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Step 4.2.2.1

Subtract $3$ from both sides of the equation.

$x = 1 - 3$

Step 4.2.2.2

Subtract $3$ from $1$ .

$x = - 2$

Step 4.3

Evaluate $y$ when $x = - 2$ .

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Step 4.3.1

Substitute $- 2$ for $x$ .

$y = (- 2) + 3$

Step 4.3.2

Substitute $- 2$ for $x$ in $y = (- 2) + 3$ and solve for $y$ .

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Step 4.3.2.1

Remove parentheses.

$y = - 2 + 3$

Step 4.3.2.2

Remove parentheses.

$y = (- 2) + 3$

Step 4.3.2.3

Add $- 2$ and $3$ .

$y = 1$

Step 4.4

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 2, 1)$

Step 5

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

$m_{1} = 0$

$m_{2} = 1$

$(- 2, 1)$

Step 6

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