Algebra Examples

3 x + 5 y - 15 = 0

$3 x + 5 y - 15 = 0$

Step 1

Rewrite in slope-intercept form.

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

Move all terms not containing

y

$y$ to the right side of the equation.

Tap for more steps...

Step 1.2.1

Subtract

3 x

$3 x$ from both sides of the equation.

5 y - 15 = - 3 x

$5 y - 15 = - 3 x$

Step 1.2.2

Add

15

$15$ to both sides of the equation.

5 y = - 3 x + 15

$5 y = - 3 x + 15$

5 y = - 3 x + 15

$5 y = - 3 x + 15$

Step 1.3

Divide each term in

5 y = - 3 x + 15

$5 y = - 3 x + 15$ by

5

$5$ and simplify.

Tap for more steps...

Step 1.3.1

Divide each term in

5 y = - 3 x + 15

$5 y = - 3 x + 15$ by

5

$5$ .

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

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

Step 1.3.2

Simplify the left side.

Tap for more steps...

Step 1.3.2.1

Cancel the common factor of

5

$5$ .

Tap for more steps...

Step 1.3.2.1.1

Cancel the common factor.

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

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

Step 1.3.2.1.2

Divide

y

$y$ by

1

$1$ .

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

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

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

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

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

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

Step 1.3.3

Simplify the right side.

Tap for more steps...

Step 1.3.3.1

Simplify each term.

Tap for more steps...

Step 1.3.3.1.1

Move the negative in front of the fraction.

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

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

Step 1.3.3.1.2

Divide

15

$15$ by

5

$5$ .

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

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

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

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

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

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

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

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

Step 1.4

Write in

y = m x + b

$y = m x + b$ form.

Tap for more steps...

Step 1.4.1

Reorder terms.

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

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

Step 1.4.2

Remove parentheses.

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

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

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

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

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

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

Step 2

Use the slope-intercept form to find the slope and y-intercept.

Tap for more steps...

Step 2.1

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = - \frac{3}{5}

$m = - \frac{3}{5}$

b = 3

$b = 3$

Step 2.2

The slope of the line is the value of

m

$m$ , and the y-intercept is the value of

b

$b$ .

Slope:

- \frac{3}{5}

$- \frac{3}{5}$

y-intercept:

(0, 3)

$(0, 3)$

Slope:

- \frac{3}{5}

$- \frac{3}{5}$

y-intercept:

(0, 3)

$(0, 3)$

Step 3

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$