Determine the y-intercept of a linear relation

The y-intercept is the value of the dependent variable when the independent variable is zero, represented by the point $(0,b)$ and, in $y=mx+b$ , by the constant term $b$ . It can be determined from an equation, table, or graph and interpreted as the initial value, while distinguishing it from the x-intercept; the focus is on ordinary linear relations, not nonlinear, piecewise, or more abstract generalized cases.

Detailed Explanation: 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 $(y=0)$ .

Learn by doing: Determine the y-intercept of a linear relation

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Linear Equations - Find Y Intercept (Decimal) - Slope Y Intercept Form

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