Skill: Write the equation of a line from its slope and y-intercept

A line with slope $m$ and $y$-intercept $b$ can be written in slope-intercept form:

$$y=mx+b$$

To write the equation:

1. Identify the slope $m$.
2. Identify the $y$-intercept $b$.
3. Substitute those values into $(y=mx+b)$.
4. Simplify if needed.

Example: Write the equation of a line with slope $(-\frac{2}{3})$ and $y$-intercept $4$.

The slope is

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

and the $y$-intercept is

$$b=4.$$

Substitute these values into the formula:

$$y=mx+b$$ $$y=-\frac{2}{3}x+4$$

So, the equation of the line is

$$\boxed{y=-\frac{2}{3}x+4}$$

The $y$-intercept of $4$ means the line passes through $((0,4))$. The slope $(-\frac{2}{3})$ means that for every $3$ units moved to the right, the line moves $2$ units down.