Precalculus Examples

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

Use the slope-intercept form to find the slope.

Tap for more steps...

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 $1$ .

$m_{1} = 1$

Use the slope-intercept form to find the slope.

Tap for more steps...

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 $5$ .

$m_{2} = 5$

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

$y = x - 4$

$y = 5 x$

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

Tap for more steps...

Eliminate the equal sides of each equation and combine.

$x - 4 = 5 x$

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

Tap for more steps...

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

Tap for more steps...

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

$x - 4 - 5 x = 0$

Subtract $5 x$ from $x$ .

$- 4 x - 4 = 0$

Add $4$ to both sides of the equation.

$- 4 x = 4$

Divide each term by $- 4$ and simplify.

Tap for more steps...

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

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

Cancel the common factor of $- 4$ .

Tap for more steps...

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $4$ by $- 4$ .

$x = - 1$

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

Tap for more steps...

Substitute $- 1$ for $x$ .

$y = 5 (- 1)$

Multiply $5$ by $- 1$ .

$y = - 5$

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

$(- 1, - 5)$

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

$m_{1} = 1$

$m_{2} = 5$

$(- 1, - 5)$

Enter YOUR Problem