Finite Math Examples

y = x - 4

$y = x - 4$ ,

y = - x + 7

$y = - x + 7$

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

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 1.2

Using the slope-intercept form, the slope is

1

$1$ .

m_{1} = 1

$m_{1} = 1$

m_{1} = 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

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 2.2

Using the slope-intercept form, the slope is

- 1

$- 1$ .

m_{2} = - 1

$m_{2} = - 1$

m_{2} = - 1

$m_{2} = - 1$

Step 3

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

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

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

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

$x - 4 = - x + 7$

Step 4.2

Solve

x - 4 = - x + 7

$x - 4 = - x + 7$ for

x

$x$ .

Tap for more steps...

Step 4.2.1

Move all terms containing

x

$x$ to the left side of the equation.

Tap for more steps...

Step 4.2.1.1

Add

x

$x$ to both sides of the equation.

x - 4 + x = 7

$x - 4 + x = 7$

Step 4.2.1.2

Add

x

$x$ and

x

$x$ .

2 x - 4 = 7

$2 x - 4 = 7$

2 x - 4 = 7

$2 x - 4 = 7$

Step 4.2.2

Move all terms not containing

x

$x$ to the right side of the equation.

Tap for more steps...

Step 4.2.2.1

Add

4

$4$ to both sides of the equation.

2 x = 7 + 4

$2 x = 7 + 4$

Step 4.2.2.2

Add

7

$7$ and

4

$4$ .

2 x = 11

$2 x = 11$

2 x = 11

$2 x = 11$

Step 4.2.3

Divide each term in

2 x = 11

$2 x = 11$ by

2

$2$ and simplify.

Tap for more steps...

Step 4.2.3.1

Divide each term in

2 x = 11

$2 x = 11$ by

2

$2$ .

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

$2$ .

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