Examples

y = 6 x

$y = 6 x$ ,

y = x + 3

$y = x + 3$

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

6

$6$ .

m_{1} = 6

$m_{1} = 6$

m_{1} = 6

$m_{1} = 6$

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 = 6 x, y = x + 3

$y = 6 x, y = x + 3$

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.

6 x = x + 3

$6 x = x + 3$

Step 4.2

Solve

6 x = x + 3

$6 x = x + 3$ 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

Subtract

x

$x$ from both sides of the equation.

6 x - x = 3

$6 x - x = 3$

Step 4.2.1.2

Subtract

x

$x$ from

6 x

$6 x$ .

5 x = 3

$5 x = 3$

5 x = 3

$5 x = 3$

Step 4.2.2

Divide each term in

5 x = 3

$5 x = 3$ by

5

$5$ and simplify.

Tap for more steps...

Step 4.2.2.1

Divide each term in

5 x = 3

$5 x = 3$ by

5

$5$ .

\frac{5 x}{5} = \frac{3}{5}

$\frac{5 x}{5} = \frac{3}{5}$

Step 4.2.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.2.1

Cancel the common factor of

5

$5$ .

Tap for more steps...

Step 4.2.2.2.1.1

Cancel the common factor.

\frac{5 x}{5} = \frac{3}{5}

$\frac{5 x}{5} = \frac{3}{5}$

Step 4.2.2.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{3}{5}

$x = \frac{3}{5}$

x = \frac{3}{5}

$x = \frac{3}{5}$

x = \frac{3}{5}

$x = \frac{3}{5}$

x = \frac{3}{5}

$x = \frac{3}{5}$

x = \frac{3}{5}

$x = \frac{3}{5}$

Step 4.3

Evaluate

y

$y$ when

x = \frac{3}{5}

$x = \frac{3}{5}$ .

Tap for more steps...

Step 4.3.1

Substitute

\frac{3}{5}

$\frac{3}{5}$ for

x

$x$ .

y = (\frac{3}{5}) + 3

$y = (\frac{3}{5}) + 3$

Step 4.3.2

Substitute

\frac{3}{5}

$\frac{3}{5}$ for

x

$x$ in

y = (\frac{3}{5}) + 3

$y = (\frac{3}{5}) + 3$ and solve for

y

$y$ .

Tap for more steps...

Step 4.3.2.1

Remove parentheses.

y = \frac{3}{5} + 3

$y = \frac{3}{5} + 3$

Step 4.3.2.2

Remove parentheses.

y = (\frac{3}{5}) + 3

$y = (\frac{3}{5}) + 3$

Step 4.3.2.3

Simplify

(\frac{3}{5}) + 3

$(\frac{3}{5}) + 3$ .

Tap for more steps...

Step 4.3.2.3.1

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

y = \frac{3}{5} + 3 \cdot \frac{5}{5}

$y = \frac{3}{5} + 3 \cdot \frac{5}{5}$

Step 4.3.2.3.2

Combine

3

$3$ and

\frac{5}{5}

$\frac{5}{5}$ .

y = \frac{3}{5} + \frac{3 \cdot 5}{5}

$y = \frac{3}{5} + \frac{3 \cdot 5}{5}$

Step 4.3.2.3.3

Combine the numerators over the common denominator.

y = \frac{3 + 3 \cdot 5}{5}

$y = \frac{3 + 3 \cdot 5}{5}$

Step 4.3.2.3.4

Simplify the numerator.

Tap for more steps...

Step 4.3.2.3.4.1

Multiply

3

$3$ by

5

$5$ .

y = \frac{3 + 15}{5}

$y = \frac{3 + 15}{5}$

Step 4.3.2.3.4.2

Add

3

$3$ and

15

$15$ .

y = \frac{18}{5}

$y = \frac{18}{5}$

y = \frac{18}{5}

$y = \frac{18}{5}$

y = \frac{18}{5}

$y = \frac{18}{5}$

y = \frac{18}{5}

$y = \frac{18}{5}$

y = \frac{18}{5}

$y = \frac{18}{5}$

Step 4.4

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

(\frac{3}{5}, \frac{18}{5})

$(\frac{3}{5}, \frac{18}{5})$

(\frac{3}{5}, \frac{18}{5})

$(\frac{3}{5}, \frac{18}{5})$

Step 5

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

m_{1} = 6

$m_{1} = 6$

m_{2} = 1

$m_{2} = 1$

(\frac{3}{5}, \frac{18}{5})

$(\frac{3}{5}, \frac{18}{5})$

Step 6

Enter YOUR Problem