Skill: Determine the y-intercept of a linear relation

The $y$-intercept is the point where a line crosses the $y$-axis. At this point, the $x$-value is always $0$.

For an equation in the form

$$y=mx+b,$$

the $y$-intercept is $b$. The intercept can be written as the point $((0,b))$.

Example

Determine the $y$-intercept of

$$y=3x-7.$$

Step 1: Identify the constant term.

Compare the equation with $(y=mx+b)$:

$$y=3x+(-7).$$

So, $(b=-7)$.

Step 2: Write the intercept as a point.

The $y$-intercept is

$$(0,-7).$$

Step 3: Check by substituting $(x=0)$.

$$y=3(0)-7$$ $$y=-7.$$

Therefore, the line crosses the $y$-axis at $\boxed{(0,-7)}$. This value, $(-7)$, is also the initial value of the relation.

Remember: the $y$-intercept occurs when $(x=0)$, while the $x$-intercept occurs when $(y=0)$.