Finite Math Examples

$y = x - 4$ , $y = - x + 7$

Step 1

Use the slope-intercept form to find the slope.

Tap for more steps...

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.

Tap for more steps...

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.

$y = x - 4, y = - x + 7$

Step 4

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

Tap for more steps...

Step 4.1

Eliminate the equal sides of each equation and combine.

$x - 4 = - x + 7$

Step 4.2

Solve $x - 4 = - x + 7$ for $x$ .

Tap for more steps...

Step 4.2.1

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

Tap for more steps...

Step 4.2.1.1

Add $x$ to both sides of the equation.

$x - 4 + x = 7$

Step 4.2.1.2

Add $x$ and $x$ .

$2 x - 4 = 7$

Step 4.2.2

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

Tap for more steps...

Step 4.2.2.1

Add $4$ to both sides of the equation.

$2 x = 7 + 4$

Step 4.2.2.2

Add $7$ and $4$ .

$2 x = 11$

Step 4.2.3

Divide each term in $2 x = 11$ by $2$ and simplify.

Tap for more steps...

Step 4.2.3.1

Divide each term in $2 x = 11$ by $2$ .

$\frac{2 x}{2} = \frac{11}{2}$

Step 4.2.3.2

Simplify the left side.

Tap for more steps...

Step 4.2.3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{11}{2}$

Step 4.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{11}{2}$

Step 4.3

Evaluate $y$ when $x = \frac{11}{2}$ .

Tap for more steps...

Step 4.3.1

Substitute $\frac{11}{2}$ for $x$ .

$y = - (\frac{11}{2}) + 7$

Step 4.3.2

Substitute $\frac{11}{2}$ for $x$ in $y = - (\frac{11}{2}) + 7$ and solve for $y$ .

Tap for more steps...

Step 4.3.2.1

Multiply $- 1$ by $\frac{11}{2}$ .

$y = - \frac{11}{2} + 7$

Step 4.3.2.2

Simplify $- \frac{11}{2} + 7$ .

Tap for more steps...

Step 4.3.2.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{11}{2} + 7 \cdot \frac{2}{2}$

Step 4.3.2.2.2

Combine $7$ and $\frac{2}{2}$ .

$y = - \frac{11}{2} + \frac{7 \cdot 2}{2}$

Step 4.3.2.2.3

Combine the numerators over the common denominator.

$y = \frac{- 11 + 7 \cdot 2}{2}$

Step 4.3.2.2.4

Simplify the numerator.

Tap for more steps...

Step 4.3.2.2.4.1

Multiply $7$ by $2$ .

$y = \frac{- 11 + 14}{2}$

Step 4.3.2.2.4.2

Add $- 11$ and $14$ .

$y = \frac{3}{2}$

Step 4.4

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

$(\frac{11}{2}, \frac{3}{2})$

Step 5

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

$m_{1} = 1$

$m_{2} = - 1$

$(\frac{11}{2}, \frac{3}{2})$

Step 6