Examples

$y = x - 4$ , $y = 5 x$

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 $1$ .

$m_{1} = 1$

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 $5$ .

$m_{2} = 5$

Step 3

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

$y = x - 4, y = 5 x$

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.

$x - 4 = 5 x$

Step 4.2

Solve $x - 4 = 5 x$ for $x$ .

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Step 4.2.1

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

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Step 4.2.1.1

Subtract $5 x$ from both sides of the equation.

$x - 4 - 5 x = 0$

Step 4.2.1.2

Subtract $5 x$ from $x$ .

$- 4 x - 4 = 0$

Step 4.2.2

Add $4$ to both sides of the equation.

$- 4 x = 4$

Step 4.2.3

Divide each term in $- 4 x = 4$ by $- 4$ and simplify.

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Step 4.2.3.1

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

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

Step 4.2.3.2

Simplify the left side.

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Step 4.2.3.2.1

Cancel the common factor of $- 4$ .

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Step 4.2.3.2.1.1

Cancel the common factor.

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

Step 4.2.3.2.1.2

Divide $x$ by $1$ .

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

Step 4.2.3.3

Simplify the right side.

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Step 4.2.3.3.1

Divide $4$ by $- 4$ .

$x = - 1$

Step 4.3

Evaluate $y$ when $x = - 1$ .

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Step 4.3.1

Substitute $- 1$ for $x$ .

$y = 5 (- 1)$

Step 4.3.2

Multiply $5$ by $- 1$ .

$y = - 5$

Step 4.4

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

$(- 1, - 5)$

Step 5

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

$m_{1} = 1$

$m_{2} = 5$

$(- 1, - 5)$

Step 6

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