Algebra Examples

$y = - \frac{2}{3} x + 6$

Step 1

Using slope-intercept form $y = m x + b$ , identify the slope $m$ .

$y = - \frac{2}{3} x + 6$

$m = - \frac{2}{3}$

Step 2

Pick any $x$ -value, then substitute into the equation and simplify to find a point on the line.

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Step 2.1

Substitute $1$ for $x$ .

$y = - \frac{2}{3} \cdot 1 + 6$

Step 2.2

Multiply $- 1$ by $1$ .

$y = - \frac{2}{3} + 6$

Step 2.3

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{2}{3} + 6 \cdot \frac{3}{3}$

Step 2.4

Combine $6$ and $\frac{3}{3}$ .

$y = - \frac{2}{3} + \frac{6 \cdot 3}{3}$

Step 2.5

Combine the numerators over the common denominator.

$y = \frac{- 2 + 6 \cdot 3}{3}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $6$ by $3$ .

$y = \frac{- 2 + 18}{3}$

Step 2.6.2

Add $- 2$ and $18$ .

$y = \frac{16}{3}$

Step 2.7

Since $y = \frac{16}{3}$ when $x = 1$ , $(1, \frac{16}{3})$ is a point on the line.

$(1, \frac{16}{3})$

Step 3

Plug in the values of the found point and the value of the slope into the point-slope form $y - y_{1} = m (x - x_{1})$ .

$y - \frac{16}{3} = - \frac{2}{3} (x - 1)$

Step 4