Examples

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

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 $4$ .

$m_{1} = 4$

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.

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

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.

$4 x + 4 = - x$

Step 4.2

Solve $4 x + 4 = - x$ 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

Add $x$ to both sides of the equation.

$4 x + 4 + x = 0$

Step 4.2.1.2

Add $4 x$ and $x$ .

$5 x + 4 = 0$

Step 4.2.2

Subtract $4$ from both sides of the equation.

$5 x = - 4$

Step 4.2.3

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

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Step 4.2.3.1

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

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

Step 4.2.3.2

Simplify the left side.

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Step 4.2.3.2.1

Cancel the common factor of $5$ .

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Step 4.2.3.2.1.1

Cancel the common factor.

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

Step 4.2.3.2.1.2

Divide $x$ by $1$ .

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

Step 4.2.3.3

Simplify the right side.

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Step 4.2.3.3.1

Move the negative in front of the fraction.

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

Step 4.3

Evaluate $y$ when $x = - \frac{4}{5}$ .

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Step 4.3.1

Substitute $- \frac{4}{5}$ for $x$ .

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

Step 4.3.2

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

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

Step 4.4

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

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

Step 5

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

$m_{1} = 4$

$m_{2} = - 1$

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

Step 6

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