Algebra Examples

$m = - \frac{1}{3}$ , $(4, 0)$

Step 1

Find the value of $b$ using the formula for the equation of a line.

Tap for more steps...

Step 1.1

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Step 1.2

Substitute the value of $m$ into the equation.

$y = (- \frac{1}{3}) \cdot x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (- \frac{1}{3}) \cdot (4) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$0 = (- \frac{1}{3}) \cdot (4) + b$

Step 1.5

Find the value of $b$ .

Tap for more steps...

Step 1.5.1

Rewrite the equation as $- \frac{1}{3} \cdot 4 + b = 0$ .

$- \frac{1}{3} \cdot 4 + b = 0$

Step 1.5.2

Simplify each term.

Tap for more steps...

Step 1.5.2.1

Multiply $- \frac{1}{3} \cdot 4$ .

Tap for more steps...

Step 1.5.2.1.1

Multiply $4$ by $- 1$ .

$- 4 (\frac{1}{3}) + b = 0$

Step 1.5.2.1.2

Combine $- 4$ and $\frac{1}{3}$ .

$\frac{- 4}{3} + b = 0$

Step 1.5.2.2

Move the negative in front of the fraction.

$- \frac{4}{3} + b = 0$

Step 1.5.3

Add $\frac{4}{3}$ to both sides of the equation.

$b = \frac{4}{3}$

Step 2

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = - \frac{1}{3} x + \frac{4}{3}$

Step 3